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OHIO STATE UNIVERSITY 

BULLETIN 


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EFFECT OF PULSATIONS ON 
FLOW OF GASES 


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BY 

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DONAL B. PHELEY 


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BULLETIN No. 24 


ENGINEERING EXPERIMENT STATION 


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STATION 


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THE ENGINEERING EXPERIMENT STATION 


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TIJE OHIO STATE UNIVERSITY 


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PUBLISHED BY THE UNIVERSITY AT COLUMBUS 




Entered aa second-class matter November 17, 1905, at the postoffice at Columbus, dhifi), under Act 


of Congress, July 16, 1894. Acceptance for mailing at special rate of postage provided for in Section 
1103, Act of October 3, 1917. Authorised July 10, 1918. 

c • r M Y 















EFFECT OF PULSATIONS ON 
FLOW OF GASES 


BY 

HORACE JUDD 

n 

PROFESSOR OF HYDRAULIC ENGINEERING 
AND 

DONAL B. PHELEY 


PUBLISHED BY 

THE ENGINEERING EXPERIMENT STATION 

OF 


THE OHIO STATE UNIVERSITY 
COLUMBUS, OHIO 



CONTENTS 

PAGE 


I. Preliminary. 3 

II. Purpose. 4 

III. Equipment. 5 

Disturbing Elements.. . 8 

Quieting Elements. 9 

Measuring Elements.11 

Orifice-head meter.11 

Meter elements used.14 

Manometers used.15 

IV. Nature of Pulsation.16 

The Photo-pulsometer.16 

Velocity Diagrams ..17 

Effect of Pulsation on Static Pressure.21 

Pressure Pulsation greater than Velocity Pulsation.21 

Analysis of Pressure diagrams.23 

Rectification of Pressure Diagrams.25 

Velocity of Pulsation.27 

V. Elimination of Pulsation .30 

Modification of Manometer Connections.34 

Effect of Type of Manometer used.38 

Maximum Percent of Error Produced by Pulsation.39 

Distribution of Pulsation as shown by Traverse.40 

Quieting Effect of Revolving Fan Section.40 

Quieting Effect of Pulsating Bag.41 

Elimination of Pulsation by Throttling.41 

Elimination of Pulsation by the Use of Volumes.42 

Effect of Varying the Shape of Volume.43 

Elimination of Pulsation by Combining Throttling with Volumes 43 
The Muffler as a Quieting Device.44 

VI. Possibility of Adjustment of Errors.45 

Effect Produced by “Dead-end” Pulsation.45 

Application of Proposed Formula to Pulsating Flow.47 

VII. Conclusions. 48 

VIII. Bibliography.51 

IX. Discussion.52 

X. Appendix A, Historical;.69 

Appendix B, Explanatory Notes;.70 

Appendix C, Tables;.76 

Appendix D, Curves and Illustrations.86 








































No. 1869 

EFFECT OF PULSATIONS ON FLOW 
OF GASES 

By Horace Judd, Columbus, Ohio 
Member of the Society 
and 

Donal B. Pheley , 1 Columbus, Ohio 
Non-Member 

The movement of gases and liquids when calculated by the existing hydraulic 
formulas 'presupposes a steady or continuous flow of the fluid. Anything which 
causes this flow to proceed in puffs, waves, or pulsations will result, by the action 
of metering devices, in errors often of great magnitude which generally do not admit 
of any adjustment, or of any definite knowledge of the amount of the error. 

The present paper discusses work undertaken under the joint direction of the 
Engineering Experiment Station of the Ohio State University and the Research 
Sub-Committee on Fluid Meters of The American Society of Mechanical Engineers, 
which had for its object (a) the study of the nature of the pulsation and (b) the dis¬ 
covery of some practical means of reducing or eliminating the pulsation or of com¬ 
pensating for its effects on the devices used for measuring fluid flow. The investi¬ 
gation was confined to the venturi meter, the orifice meter, the flange nozzle meter, 
and the pitot meter, using air flow from a small compressor discharging into a S^in. 
line. It is believed, however, that the basic principles established by the experiments 
are fundamental for pulsating-flow conditions for gas, steam, and water as well as 
for air, and also for other sizes and kinds of installations. 

/"ANE of the most disturbing factors encountered in recent years 
^ in the metering of air, gas, steam, and water, especially in 
connection with all forms of power engineering, has been that due 
to turbulent or pulsating flow. This has not been confined to any 
one class or type of meter, but is present to a more or less degree 
with all forms of metering devices. 

2 The measurement of gases and liquids when calculated by 
the existing hydraulic formulas presupposes a steady or continuous 

1 Robinson Research Fellow, The Ohio State University. 

Presented at the Annual Meeting, New York, December 4 to 7, 1922, 
of The American Society of Mechanical Engineers. 

3 




4 


EFFECT OF PULSATIONS ON FLOW OF GASES 


flow of the fluid. Anything which causes this flow to proceed in 
puffs, waves, or pulsations will result, by the action of metering 
devices, in errors often of great magnitude which generally do not 
admit of any adjustment, or of any definite knowledge of the 
amount of the error. 

3 The work described in the present paper was undertaken 
under the joint direction of the Engineering Experiment Station 
of The Ohio State University, and the Research Sub-Committee 
on Fluid Meters of The American Society of Mechanical Engineers. 
A sub-committee of the Fluid Meters Committee consisting of 
A. R. Dodge, H. N. Packard, and H. Judd was selected to take 
direct charge of the research work. 


PURPOSE OF THE INVESTIGATION 

4 The object of the investigation as outlined by the sub¬ 
committee in direct charge was twofold: 

a To study the nature of the pulsation 
b To discover some practical means of reducing or eliminat¬ 
ing the pulsation, or of compensating for its effects on 
the devices used for measuring fluid flow. 

5 As the work has proceeded it has been necessary to use 
a specific installation involving the flow of air only, and also to 
limit somewhat the scope of the investigation. The work is by no 
means considered to be complete, and it is the intention in the 
future to continue with the research so as to shed more light on 
many doubtful points that have arisen, as well as to try out a 
number of new suggestions. 

6 For convenience, flow meters have been classified in two 
main divisions which may be called (1) positive meters, and (2) 
inferential meters. The domestic gas, or water, meter is an example 
of the first class. It is a displacement meter in which an actual 
volume of gas is introduced into a container of known size, and the 
quantity thus measured is registered on the meter. 

7 In commercial installations of even moderate size, inferen¬ 
tial meters are used almost entirely. In meters of this class some 
function of the quantity of fluid passing a given cross-section of 
pipe is measured and from this observation the actual flow is de¬ 
duced or “ inferred.” Perhaps the most common function observed 


HORACE JUDD AND D. B. PHELEY 


5 


in such meters is a pressure difference which is a quadratic function 
of the velocity of flow. This method can be made to give accurate 
results under steady-flow conditions, but when the flow is pulsating 
the accuracy of the measurement is seriously affected, if, indeed, 
not entirely destroyed. 

8 Three general cases may be mentioned where this problem 
is of great importance: (1) The measurement of natural gas, both 
entering and leaving a compressor station where reciprocating com¬ 
pressors are used; (2) the measurement of air both entering and 
leaving large reciprocating air compressors, or blowing engines; 
and (3) the measurement of steam supplied to reciprocating steam 
engines. The steam flow is pulsating in character because the en¬ 
gine cuts off the steam supply during a considerable part of each 
stroke. In each of these cases the flow of the fluid has a regular, 
comparatively rapid, rhythmical pulsation, which occasions serious 
errors in measurement, especially where the measuring element is 
of the inferential type. 

9 Similar pulsating conditions are present in water flow where 
reciprocating pumps are used. The problem, however, is more 
easily solved by the proper use of air chambers and surge tanks. 
Water hammer in pipe lines from whatever cause bears a striking 
similarity to the pulsating effect produced by an air-compressor 
valve. 

10 We have confined our investigations to inferential meters. 
These meter elements as selected are the venturi meter, the orifice 
meter, the flange nozzle meter, and the pitot meter. Furthermore, 
we have been limited to air flow from a small compressor discharg¬ 
ing into a 3-in. line; and hence our findings, strictly speaking, 
would be applicable only to installations of similar character. 
However, it would seem highly probable that the basic principles 
established by these experiments would be fundamental for pulsat- 
ing-flow conditions for gas, steam, and water as well as for air, 
and also for other sizes and kinds of installations. 

EQUIPMENT EMPLOYED IN THE INVESTIGATION 

11 The experimental work was carried on in the Mechanical 
Engineering Laboratories of the Ohio State University, and was 
begun in May, 1920. A large part of the work was done during the 
summer vacations of 1920—1921. During the remainder of the two 
years devoted to the work such time was put in as could be spared 


6 


EFFECT OF PULSATIONS ON FLOW OF GASES 




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Fig. 1 General Layout of Apparatus — Left-Hand Portion 













































































































A ARRANGEMENT OF LINE FOR GENERAL TESTS 


HORACE JUDD AND D. B. PHELEY 



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EFFECT OF PULSATIONS ON FLOW OF GASES 


from the university schedule. Acknowledgment should be made 
of the valuable service rendered by Mr. Paul Bucher, 1 especially 
during the vacation periods. 

12 The essential elements for carrying on our project were: 
(1) a disturbing element to produce the pulsating flow; (2) a 
quieting element, or elements, to eliminate or modify the pulsa¬ 
tions; and (3) a measuring element, to indicate constant flow con¬ 
ditions and also to indicate the effect of the pulsating flow. 

13 Disturbing Elements. Fig. 1 shows the general layout of 
the apparatus, at the extreme left hand of which is located the air 



compressor C, a 9-in. by 9-in. single-stage, single-acting, gas engine- 
driven machine running at 293 r.p.m. This supplied air to a line 
about 120 ft. in total length of which 50 ft. was made up of 2^-in. 
pipe containing several short lengths and fittings. The remaining 
70 ft. comprised the 3-in. test line of straight continuous length. 
This test line was at first made up of standard 3-in. black pipe of 
commercial quality; later 24 ft. of 3-in. brass pipe was substituted 
for that portion of the test line preceding the meter and extending 
3 ft. below the meter section. (See Fig. 1, B.) 

14 This air supply with its full pulsating effect could be ad¬ 
mitted directly to the^test line or could be first discharged through 
a large tank before entering the test line. A second disturbing 
element for producing pulsations artificially is shown at I, Fig. 1, 
the butterfly-valve interrupter. This butterfly valve could be 

1 Assistant Professor of Steam Engineering, The Ohio State University. 




























HOIIACE JUDD AND D. B. PHELEY 


9 


driven at speeds ranging from 180 r.p.m. to 800 r.p.m., producing 
thereby a variation in the number of pulsations per second. 

15 Quieting Elements. Considerable study was made of this 
essential feature and many trials were made to satisfy ourselves 
that we were securing pulsationless flow where and when needed. 
The tank T, Fig. 1, was used to quiet the pulsation before the meter 
station, M, was reached. This was a 48-in. vertical tank of 200 
cu. ft. capacity. Air could be admitted either at the bottom or at 
the top and released from the tank through the internal pipe which 



Fig. 3 Flow-Meter Units 


reached nearly to the top. This tank when fitted with lj-in. orifices 
at top and bottom enabled us to get air flow free from pulsations 
before the test meters were reached. 

16 A second quieting tank was inserted at Q , Fig. 1, at a 
point 8 ft. below the meter station. This was necessary in order 
to secure pulsationless flow at the orifice head for the purpose of 
establishing standard flow conditions. This tank was selected 
almost by chance and afterward was proved by test to be of suf¬ 
ficient capacity to eliminate practically all of the effect of the 
pulsating flow, and with the insertion of a 1J in. orifice at the exit 
from the tank we were entirely successful in securing pulsationless- 
flow conditions. 





10 


EFFECT OF PULSATIONS ON FLOW OF GASES 


17 There are two positions marked, V, Fig. 1, one near the 
compressor and one just beyond the large quieting tank, where 
volumes of different sizes were inserted for the purpose of studying 
their quieting effect. Because the term volume seems to apply 
better we have perverted the word “ volume ” from a term meaning 
capacity to a special designation, and have used it altogether to 
denote the various tanks of different dimensions which have been 



Fig. 4 Section Sketches of Meters, Manometers, and Connections 


used as quieting elements. Most of these volumes were used in the 
second volume space, V , beyond the large quieting tank. 

18 The line valve near the entrance to the 3-in. test line 
was used as a quieting element when employed as a throttling 
device. Both a gate valve and a globe valve and in some cases 
orifices were thus used as throttling devices. 

19 The combination of throttling with volumes constitute the 
muffler type of quieting device. Fig. 7 shows an 8-section pipe- 
flange muffler which was also inserted in the line at the second 
volume station. This muffler is located in a by-pass in front of the 
line which runs directly from the compressor. All the volumes used 


















































HORACE JUDD AND D. B. PHELEY 


11 


as quieting devices were placed in direct line, but later it was found 
that the by-pass position answered just as well for the muffler or 
the other quieting devices. Fig. 9, Nos. 1, 2, 3, 5, 6, shows some 
of the disks which were tried in the muffler. Fig. 8 shows sectional 
views of the pipe-flange muffler and also other forms of mufflers, 
including two funnel mufflers. A form of pulsating bag, Fig. 6, 
was used as a quieting volume and was connected to the compressor 



Fia. 5 Manometers Used with Flow-Meter Units 

line in a way similar to an air chamber on a reciprocating pump. 
Another form of device used was a system of revolving fans or 
baffles. (See Fig. 9, No. 7.) 

20 Measuring Elements. Under this heading will be taken 
up in order: (1) the orifice-head meter, (2) meter elements used, 
and (3) manometers used. 

21 Orifice-Head Meter. It was recognized at the outset that 
one of the indispensable features was an accurate method of measur- 








12 


EFFECT OF PULSATIONS ON FLOW OF GASES 


ing the discharge of the pipe, or (its equivalent) an accurate means 
of indicating the velocity of the air in the pipe. This was effected 
by means of an orifice head at the end of the pipe line, Fig. 1, H. 
Fig 2 is a detailed sketch of the orifice head. Its outer diameter 
is 9 in. for a distance of 2 ft., followed by a tapered section to meet 
the 3-in. line. This is given a taper of 7 deg., and was so chosen 



Fig. 6 Pulsating Bag 


as being the limiting 1 angle for preventing as far as possible the 
swirling and eddying of the air as it passes into the orifice head 
from the line. Seven holes, reamed to 1^ in., were provided in the 
head plate in. thick), although during the tests not more than 

1 Trans. Am.Soc.M.E., vol. 42, 1920, p. 26: Physical Basis of Air Pro¬ 
peller Design, F. W. Caldwell and E. N. Fales. 







HORACE JUDD AND D. B. PHELEY 


13 


five holes were used at one time. In general the capacity of the 
compressor was reached with four holes open with a standard 
static discharge head of 0.9 in. of water at the orifice head. The 
orifice head was calibrated by discharging air through it from the 
calibrated tank T under a constant static head at the orifice head. 
Readings every fifteen seconds were taken of this static head at 
the orifice head, giving 25 to 45 readings per run. The formula 
for a single orifice is: 

q = KAV = 0.1261 K V h/W a 

where q = air flowing cu. ft. per sec. 

K = coefficient of discharge 
h = static head at orifice head, inches of water 
W a = weight of 1 cu. ft. of air at temperature of flowing air 
at orifice plate. 

For separate, single orifices the maximum value for K = 0.6269, 
the minimum, K = 0.6037; average for 13 runs, K m = 0.6086. For 
orifices in combinations of twos, threes, fours, and fives, average 
of K for 22 runs including the single orifices = 0.6115. 

22 The orifice head was also checked against a second orifice 
to show how uniformly the air was distributed in its cross-section. 
A variation was found between the center orifice and the surround¬ 
ing single orifices ranging from 0.1 per cent below to 0.2 per cent 
above the ratio for the center orifice. The perforated baffles were 
then put in. These were two in number, the first being made up 
of a £-in. wooden strip screen with ^-in. openings. Two inches in 
front of this wooden screen was placed a second perforated iron 
plate with 600 J-in. holes (see Fig. 2). All possible combinations 
of the orifices including single orifices and 5-hole orifices with and 
without the center orifice gave a variation not exceeding 0.1 per cent. 
This established uniform flow conditions in the orifice head regard¬ 
less of the number of orifices open in the head plate. 

23 For the standard 3-in. pipe (inside diameter, 3.068 in.) 
with a manometer head at the orifice head of 1 in. of water, barom¬ 
eter 29.50 in., humidity at 75 per cent, the velocity of air in the 
pipe for each orifice has been calculated as follows: 



14 


EFFECT OF PULSATIONS ON FLOW OF GASES 


Temperature of air, deg. fahr. 

Velocity of air in pipe, ft. per sec. 

50 

5.49 

60 

5.55 

70 

5.61 

80 

5.67 

90 

5.73 


Wherever mention is made of the velocity of air in the pipe we 
have assumed 5.35 ft. per sec. for each orifice for a standard orifice 
head of 0.9 in. of water at 75 deg. fahr. 

24 Meter Elements Used. The point of insertion of the meter 
elements in the line, Fig. 1, M, was about 70 ft. from the com¬ 
pressor, 50 ft. above the orifice head, and 25 ft. from the entrance 
to the 3-in. test line. 

25 The venturi meter was a standard unit with 3-in. entry and 
1-in. throat. It is shown attached to the pipe line in Fig. 3, No. 1, 
and in sectional view in Fig. 4, A. 

26 The orifice meter, Fig. 3, No. 2, was made up of a flanged 
section of 3-in. brass pipe of the same length, 35 in., as the venturi 
section. The orifice flange, Fig. 4, B, was placed 12 in. from the 
upstream end and was counterbored to receive the set of orifice 
plates and to center them accurately. The downstream side of 
the hole in each plate was chamfered to ^ in. in thickness, Fig. 3, 
No. 3. 


Ratio of orifice and pipe diameters, per cent 

Size of orifice plates: Diameter of orifice, in. 

33 

1.098 

40 

1.224 

50 

1.530 

60 

1.836 

70 

2.142 

80 

2.448 

90 

2.754 

100 

3.060 


The manometer connections were made at one diameter above and 
one-half diameter below the orifice plate as the standard points 
of connection. 

27 The flange nozzle meter was made by inserting in the 
orifice-meter section a special-shaped rounded-edge orifice with 
projecting cylindrical end, as in Fig. 3, Nos. 4 and 6. This nozzle 
















HORACE JUDD AND D. B. PHELEY 


15 


approximates the converging part of the venturi tube in shape. 
The manometer connections were made at one diameter above and 
one-half diameter below the flange, corresponding to the standard 
points of connection of the orifice meter. 

28 Two forms of pitot tips were used. Fig. 3, No. 5, shows 
the hatchet-edge static tip (pitot No. 1) with -J-in. side openings. 
This is used with the accompanying open-ended impact tip with 
^.-in. opening. Both tubes are made of J-in. seamless brass tubing. 
Fig. 3, No. 7, shows a modified form of pitot tip (pitot No. 2) 
having ^-in. brass tubing and an impact or leading opening facing 


TABLE 1 SIZE OF FLANGE NOZZLES 


Diam. of nozzle, 
in. 

Inlet diameter 
at rounded edge, 
in. 

Length,in. 

Rounded 

edge 

Cylindrical 

end 

Total 

1* 

3 

1 

2.375 

3.375 

H 

3 

1 

2.375 

3.375 

2 

3 

1 

2.375 

3.375 

2i 

3 

I 

2.750 

3.375 


the direction of flow and a static or trailing opening directly oppo¬ 
site. The diameter of each opening is £ in. 

29 Manometers Used. As far as possible the simpler forms 
of manometers were used. The vertical U-tube water manometer, 
as in Fig. 5, No. 1; Fig. 4, D; Fig. 10, S, was used with the venturi 
meter, and part of the time with the orifice meter and flange nozzle 
meter, and also for the static line pressure. Where the readings 
had to be magnified, use was made of a 6-in. inclined one-leg reser¬ 
voir oil manometer, 5 to 1 magnification (Fig. 5, No. 2; Fig. 4, C). 
For certain other readings an inclined U-tube oil manometer and 
a vertical U-tube two-liquid manometer were used (Fig. 5, Nos. 
3 and 4). 

30 A Foxboro differential mercury recording gage, Fig. 5, 
No. 5 and Fig. 4, E y was used to make comparisons with the water 
manometer used with the venturi meter. The flow conditions were 
maintained and checked at the orifice head by means of an Ellison 
inclined gage of 1 in. range and 10 to 1 magnification. 













16 


EFFECT OF PULSATIONS ON FLOW OF GASES 


NATURE OF THE PULSATION 

31 The first knowledge of the nature of the pulsation was 
gained through the use of an instrument which we have called the 
“ photopulsometer.” This instrument was made and loaned to us by 
Mr. H. N. Packard of the Cutler-Hammer Co., Milwaukee, Wis. 
Its principle is similar to that of the “ phonedeik ” designed by 
Prof. D. C. Miller 1 of Case School of Applied Science and used by 
him in photographic studies of musical sounds. 



Fig. 7 Eight-Section Pipe-Flange Muffler 

32 The photopulsometer is shown in the diagrammatic sketch 
of Fig. 11. A pitot-tube with one leading and one trailing tip set 
with the opening in line on a vertical diameter was inserted in the 
center of the pipe. The leading or impact tip communicated with 
the under side of a diaphragm chamber. The trailing or static tip 
led to the upper side of the diaphragm chamber. The mica dia¬ 
phragm, 0.011 in. thick, would therefore respond to changes in 
velocity of the air in the line as they occurred. These vibrations 
1 The Science of Musical Sounds, p. 78, D. C. Miller. 







HORACE JUDD AND D. B. PHELEY 


17 


were directly transmitted to a mirror hung in jeweled bearings and 
by means of a beam of light could be thrown on a photographic 
film giving a diagram proportional to the velocity. By means of 
a pendulum beating quarter- and half-seconds a chronographic 
record could also be made as shown on most of the films, for ex¬ 
ample in Fig. 14, by the breaks in the diagrams. A great many 
films were taken in this manner under a number of different run¬ 
ning conditions and it proved to be a valuable method for providing 
a permanent record of the state of the flowing air in the line, either 
under violent pulsations due to various disturbing factors or for 



Fio. 8 Muffler Devices 


more steady flow due to the effect of certain quieting factors, as 
well as a record of the state of flow when under steady or pulsation- 
less-flow conditions. 

33 Velocity Diagrams. Figs. 12 to 19, inclusive, give records 
of the velocity changes at the center of the pipe line at various 
points and under various flow conditions. The maximum effect 
of the pulsation in the open line direct from the compressor is 
shown in Fig. 12. There is little or no quieting effect due to a 

length of pipe equal to 183 diameters. As measured from the 

diagrams: 

Average of maximum pulsation at 50 ft. from compressor = 1.05 

Average of maximum pulsation at 111 ft. from compressor = 0.80 

Square root of ratio of 80 to 105 = 0.875. 























































































18 


EFFECT OF PULSATIONS ON FLOW OF GASES 


This equals 12.5 per cent quieting effect due to length of pipe for 
a maximum error of 82 per cent due to pulsating flow. 

34 Fig. 13 shows artificial pulsations as produced by the 
butterfly-valve interrupter and that they are much less violent 
than those shown in the previous figure where the valve to the com¬ 
pressor is an automatic valve with a light spring. Diagrams (a) 



Fig. 9 Muffler Disks, Fan Units, and Small Quieting Devices 

and (b) approach more nearly the shape of a sine curve. It should 
be noted that whenever the interrupter was used the air supplied 
came from the tank T, Fig. 1, used as a storage tank. The air 
was therefore free from pulsations except those that were imparted 
by the interrupter itself. 

35 In Fig. 14 are shown artificial pulsations which are 
most violent near the interrupter. Those from a point 4 ft. 
[Diagram (a) ] above the interrupter show only a slight disturbance 
indicating that the pulsation is retarded somewhat by the flowing 
current of air. Diagram (d), taken beyond the 24-in. volume, 




HORACE JUDD AND D. B. PHELEY 


19 


shows its quieting effect and also shows the kind of diagram to be 
expected for pulsationless-flow conditions. 

36 Diagram (a ), Fig. 15, also shows pulsationless-flow condi¬ 
tions when the violent pulsations direct from the compressor have 
been eliminated by the use of the big tank T as a quieting device. 



Fig. 10 Manometer for Pressure in Line 

Diagram (b) shows that the diaphragm of the photopulsometer is 
not affected by the sound waves from a phonograph. Diagram (c) 
was taken to determine the natural period of vibration of the 
photopulsometer. This shows 6 vibrations in 0.103 sec., or 58 
vibrations per second. This will explain the minute secondary pul¬ 
sations occurring in Diagram (a) and in others under pulsationless 








20 


EFFECT OF PULSATIONS ON FLOW OF GASES 


flow. Most of the secondary pulsations seen in the other diagrams 
are likewise due to the same cause. Due to this cause also, some 
of the diagrams appear to go below the zero line when in reality 
they do not. Some other cases arise, however, where the pulsation 
appears to be negative, for which no good reason could be assigned. 

37 The large tank T was tried as a quieting chamber, when 
connected similar to an air chamber to a pump. Fig. 16 shows 
that such an arrangement is worthless as a quieting device. This 



substantiates our later experience that, to be effective, tanks, or 
volumes, should be inserted in the line so that the air may pass 
through them axially. 

38 One of the methods for eliminating pulsations is throttling 
by means of some kind of obstruction in the line such as a valve 
or an orifice. Diagram (a), Fig. 17, is taken for maximum pulsa¬ 
tions direct from compressor. The diagrams appear to go below 
the zero pressure line, but when the secondary pulsations due to the 
natural period of vibration of the diaphragm are considered, it 































HORACE JUDD AND D. B. PHELEY 


21 


will be seen that the true diagrams approach but do not go below 
the zero line. Diagram (6) shows the quieting effect of an orifice 
when the pulsation has been reduced to the condition of pulsation¬ 
less flow. 

39 Effect of Pulsation of the Static Pressure in the Line. For 
a compressor speed of 293 r.p.m., or nearly five revolutions per 
second, and for an air velocity in the pipe from 22 to 27 ft. per sec., 
the velocity wave length as shown by the diagrams would be from 
4 to 6 ft. On starting the compressor it seemed frequently that 
the first impulse traveled much faster than the actual velocity 
of the air. 

40 • Pipe-Line Pressure Diagrams. To test this out and also 
to study the effect of pulsation on the static pressure in the line, 
two Crosby indicators were attached to the line, one on the com¬ 
pressor cylinder (Fig. 1 , C) , and the other 70 ft. distant (Fig. 1 , A, 
No. 1 indicator) near the meter space. For details of arrange¬ 
ment of indicators for taking simultaneous pressure readings, see 
also Fig. 1 , B. Diagrams from the compressor cylinder (Fig. 20, A, 
No. 1) had been taken several times before this as had also dia¬ 
grams on indicator at point No. 1, Fig. 1, to show the rapid fluctua¬ 
tion in static pressure. When the indicator at point No. 1 was 
moved by hand a diagram was obtained closely resembling that 
shown on the films from the photopulsometer; but no diagrams had 
been taken simultaneously. 

41 Since the sudden rise in the diagram taken by indicator 
No. 1 must mark the beginning of a pulsation, it was concluded 
that this initial point was the point at which the valve opened 
on the compressor, thus releasing a pulsation into the air line. 
This pulsation would continue with the upward stroke of the piston 
and at the instant that the valve on the compressor closed the 
pulsation on the record would cease. 

42 The two indicator drums were connected by means of a 
light piano wire to the reducing motion on the engine. The two 
indicator pencil motions were connected by an electric circuit 
operating a detent motion. The pencil motion on the indicator at 
the compressor closed a switch and by means of a solenoid operated 
the pencil motion of the second indicator. Whenever simultaneous 
cards were taken, this method was used. 

43 Pressure Pulsation Greater Than Velocity Pulsation. 
Three sets of such diagrams were taken and are shown at A and B, 
Fig. 20. Two important features were brought out: (1) The pulsa- 


22 


EFFECT OF PULSATIONS ON FLOW OF GASES 


tion in the pipe produced a much greater pressure effect than that 
imparted to the velocity of flow. The diagram taken with the pitot 
tip (Fig. 20, B, No. 2) would be expected to give the combined 
effect due to pressure and velocity; and a larger and somewhat 
modified diagram might be looked for. On the contrary, the two 
diagrams taken with the static connection and with the pitot tip 
are strikingly similar in shape. (2) When simultaneous diagrams 
for a single stroke were recorded (Fig. 20, A and B, No. 3) it was 
found that the suction stroke of the compressor corresponded to 
the pressure stroke in the line. This seemed to indicate that the 



Fia. 12 Showing Maximum Effect of Pulsations at Different Points on 
the Line — No Quieting Effect Due to Increase in Length of Line 

(a) Maximum pulsation in line 50 ft. below compressor. (6) Do., Ill ft. below compressor. 


pulsation required about the time of a compressor revolution to 
travel a distance of 70 ft. in the pipe. For a speed of 291 r.p.m. 
this would mean about 0.1 sec. for £ revolution, or a pulsation 
velocity of 700 ft. per sec. 

44 To verify this assumption, two more indicators were added 
and their location rearranged as shown in Fig. 1, A and B. The 
one at the compressor remained unchanged, a second (at O, Fig. 
1, A) was placed 18 in. distant in the discharge line to establish the 








HORACE JUDD AND D. B. PHELEY 


23 


beginning of pulsation (see Cards 14c, 14o, Fig. 21); indicators I 
and II (Fig. 1, B) were placed in the 3-in. line, 54 ft. and 84 ft., 
respectively, from the compressor. They were connected to the 
detent motion through the electric circuit and were arranged so as 
to be operated either by hand or by the reducing motion. In addi¬ 
tion, sparking points were attached to indicators I and II and to 
the secondary coil, grounded through the pipe line, so that, by 
means of a commutator, the cards on Nos. I and II would be per- 



Fig. 13 Pulsations Produced Artificially by Butterfly-Valve Interrupter. 
Velocity of Air in Line, 27 Ft. per Sec. 

(o) 53 ft. below interrupter, 3 pulsations per sec. (6) 53 ft. below interrupter, 4 pulsations per 
sec. (c) 53 ft. below interrupter, 13.5 pulsations per sec. 


forated simultaneously by twelve sparks for each revolution of the 
drum while operated by hand. (See Fig. 21, Cards ll x , ll n .) 

45 Analysis of Pressure Diagrams. Fig. 21 comprises dia¬ 
grams traced from cards taken on these indicators, including 
simultaneous cards at points C and 0, C and I, C and II, C, I and 
II, and cards taken at I and II with coincident points shown by 
spark points. These diagrams include: 

a Partial cards for establishing the fact that the initial point 




24 


EFFECT OF PULSATIONS ON FLOW OF GASES 


of pulsation is the initial point of pressure rise in the line which 
is seen to correspond to the point of valve opening in the com¬ 
pressor. (See diagrams to establish simultaneous pressure points, 
Cards 6 c, 60 , 14c, 14o) 

b Complete diagrams plotted in one direction, showing the 
use of the coincident lines. The drums were moved by hand and, 



Fig. 14 Showing Artificial Pulsations at Different Points in the Line 


Distances from butterfly-valve interrupter: (o) 4 ft. above; (6) 0.5 ft. above; (c) 2 ft. below 
(d) 60 ft. below, showing quieting effect of 24-in. volume. 


at several points, simultaneous lines were drawn by means of the 
detent motion. This gives a method of accurate comparison of 
selected pulsations. 

c Also hand-operated diagrams to illustrate the initial pulsa¬ 
tion points for repeated pulsations. The identity of the simulta- 









HORACE JUDD AND D. B. PHELEY 


25 



neous strokes on the indicators is established and shown by means 
of the arrows of direction. (See Cards 3c, 3o.) 

46 For the hand-operated cards the simultaneous lines are 
numbered alike and the initial points on the same pulsation at 
different points as it progresses are lettered AAA, BBB, CCC, etc. 
The progress of the pulsation down the pipe is shown clearly and 
the similarity of the shape as compared with the record from the 
photopulsometer is also apparent. (See Cards 3c, 3 I} 3 n ; 11 I? ll n ) 


Fig. 15 Showing Velocity Conditions tor Pulsationless Flow, and the 
Natural Period of Vibration of the Diaphragm 

(а) Taken 111 ft. below compressor; air flowing from tank, no pulsations; velocity of air 
in line, 27 ft. per sec. 

(б) Taken with tips placed in front of phonograph, sound concentrated in convergent nozzles. 

(c) Showing the natural period of vibration of the photopulsometer. 

47 Rectification of Pressure Diagrams. A few diagrams have 
been plotted to a uniform horizontal scale, or in other words, the 
diagrams have been converted into pressure-time diagrams. This 
method is clearly shown in Fig. 22. The motion of the piston has 
been considered as that of simple harmonic motion, which is not 
strictly true, owing to the finite length of the connecting rod. By 
plotting the complete pulsation as if the diagrams were taken in 




( 



w 

♦-H 

Ah 

£ 

£ 

o 

►H 

H 

<3 

P 

Ah 

Ah 

O 

Jh 

H 

£ 

O 

H 

> 


ci 


W 

A3 

<3 

H 


•8 


fc 

H 

W 

g 

H 

a 

« 

fc 

O 

►H 

◄ 

CD 

i-3 

P 

Ah 

a 

o 

*M 

►H 

o 

o 

a 

a 

> 

a 

o 

ao 

fc 

O 

M 

H 

H 

P 

a 

s 

o 

O 


\ 


EFFECT OF PULSATIONS ON FLOW OF GASES 


Remarks 

CO 

& 

<N 

II 

s 

d 

pi 

✓-^--N 

Number 

of 

holes at 
orifice 
head 

4—3.4.6.7. 

4- 

4- 

4- 

3-4.6.7. 

3 

3 

3 

Velocity 
of pulsation, 
ft. per 

sec. 

1052 

1185 

1135 

1028 

985 

930 

928 

1106 

Time taken 
by pulsation 
to travel 

30 ft. 

0.0285 

0.0253 

0.0264 

0.0292 

0.0305 

0.0323 

0.0224 

0.0271 

Lead 

I-II 
lOOths 
of an inch 

OCiCOCJHHtON 

H rH rH 

Distance from 
beginning of pulsation 
to reference line 

HH 

OO^ONWNOOf/' 

HH 

OOCOOOCD^CC^iO 

Value of 
0.01 in. 
in seconds 
of time 

0.00285 

0.00281 

0.00330 

0.00325 

0.00277 

0.00293 

0.00373 

0.00387 

Length of 
pulsation 
in lOOths 
of an 
inch 

<NCO<NcO^OiOCO 

Pulsation 

measured 

OHhOfflDflh 

i i i i i i i i 

OQBhCffloW 

Coin¬ 

cident 

line 

^cooo05co>ono 

rH 

Card 

No. 

O O O © rH rH rH rH 
rHrHrHrHrHrHrHrH 


■8 


O 

CD 

tf 

O 

◄ 

o 

>-< 

Q 

Z 


z 

a 

a 

& 

a 

« 

55 

O 

H 

H 

◄ 

go 

a 

P 

Ph 

a 

o 

& 

H 

o 

o 

a 

a 

t> 

a 

o 

oo 

Z 

O 

H 

H 

P 

a 

a 

o 

u 


Velocities, ft. per sec., 

based on distance 

30 ft. 

1640 

941 

1095 

1148 

1465 

809 

84 ft. 

1950 

893 

1330 

1190 

1230 

797 

54 ft. 

1830 

869 

1510 

1210 

1130 

791 

Time taken by pul¬ 

sation to travel 

30 ft. 

0.0183 

0.0319 

0.0274 

0.0261 

0.0205 

0.0371 

84 ft. 

0.0480 

0.0941 

0.0632 

0.0706 

0.0683 

0.1052 

54 ft. 

0.0296 

0.0662 

0.0359 

0.0446 

0.0478 

0.0683 

Lead in lOOths 
of an inch 

1 

o 

13 

19 

16 

14 

15 

19 

C-II 

34 

56 

37 

38 

50 

54 

C-I 

H N H lO iO 

<M CO <N <N CO CO 

Distance from be- 
ginning puls, to line 

HH 

HH 

O ^ lO ^ 00 (M 

rH 1 rH rH 

1 1 1 

HH 

CO 1C H 00 CO h 

H w H | 

O 

24 

52 

42 

42 

32 

42 

Value of 
0.01 in. 
in seconds 
of time 

0.00141 

0.00168 

0.00171 

0.00186 

0.00136 

0.00195 

* i 

Length of 
pulsation 
in lOOths 
of an inch 

145 

122 

120 

110 

150 

105 

Pulsa¬ 

tion 

mea¬ 

sured 

WOBOfqO 

i 1 l i 1 l 

<1 « <3 « < m 

Coin¬ 

cident 

line 

<N CO CO © CO 

Card 

No. 

lO iO CO O N N 
















































































HORACE JUDD AND D. B. PHELEY 


27 


one direction only, the true characteristic shape of the pressure 
diagram is obtained. When the pulsation is foreshortened and re¬ 
peated it bears a striking resemblance to those shown on the hand- 
operated diagrams in Fig. 22 and shown also on the film of the 
photopulsometer. 

48 The Velocity of the Pulsation. The determination of the 
velocity of pulsation from the simultaneous sets of indicator dia¬ 
grams for points I and II located 30 ft. apart was made as follows: 

a Hand-operated diagrams were taken as previously ex¬ 
plained. 

b The diagrams were carefully compared, points of spark 
puncture located, coincident lines drawn thereform and numbered, 
and the initial points of the pulsations were identified and marked 
AAA, BBB, CCC, etc. The unavoidable irregularity of hand 
operation rendered the identical pulsations easily recognizable by 
means of their relative lengths. 

c Measurements of the sets of diagrams were carried out, 
as shown in Table 2. It will be noticed that the computations 
shown include some of the diagrams illustrated in Fig. 21. All 
the diagrams shown are tracings of originals and are numbered 
and dated. 

d Results were computed as shown on Table 2. Choosing 
Diagram 11 (see Fig. 21, Cards 11);, coincident line No. 3, pulsa¬ 
tion A-B is 0.74 in. long. For 293 r.p.m. one revolution = 0.205 
sec. = time of one pulsation. If 0.74 in. or one pulsation = 0.205 
sec., 0.01 in. = 0.00277 sec. Point A is 0.24 in. from line 3 for 
indicator I, and is 0.13 in. from line 3 for indicator II, a lead at 
point I over point II of 0.11 in., or the time taken to travel 30 ft. 
will be 0.00277 x 11 which is 0.0305 sec. Rate of travel per second 
= 30 0.0305 = 985 ft., which is the velocity of pulsation. The 

velocity of sound in dry air at 0 deg. cent., 766 mm. pressure, is 
1086 ft. per sec. 

49 Table 3 gives the average results computed as in the 
example given and includes data taken for three points in the line, 
30 ft., 54 ft. and 84 ft. from the compressor, and for six different 
velocities of air flow. 

50 These results establish three significant facts: 

a That, although our method shows results varying from the 
maximum to the minimum through a wide range, yet in no case 


28 


EFFECT OF PULSATIONS ON FLOW OF GASES 


does the velocity of pulsation so determined approach anywhere 
near the velocity of the flowing air. 

b That, for a variation of velocity of flowing air ranging from 
zero to 27 ft. per sec., the velocity of pulsation was found to be 
independent of the velocity of the air. 

c That the total average for 148 computations gave 1090 ft. 
per sec. as the velocity of pulsation. The velocity of sound in dry 
air at 32 deg. fahr. and 29.92 in. barometer is 1083 ft. per sec. The 
velocity of pulsation in all probability is equal to that, of sound 
in air. 


TABLE 3 AVERAGE RESULTS FOR VELOCITY OF PULSATION 


Date 

No. 

Number of 
diagrams 
measured 

Length of 
pipe used, 
ft. 

Velocity 
of air per 
sec., ft. 

Velocity of pulsation, 
ft. per sec. 

Max. 

Min. 

Avg. 

4-5-22 

1 

14 

30 

0 

1462 

640 

1042 


2 

16 

30 

5 

1412 

869 

1088 


3 

18 

30 

11 

1440 

805 

1124 


4 

20 

30 

16 

1263 

775 

1019 


5 

20 

30 

22 

1290 

815 

1044 


6 

13 

30 

27 

1465 

747 

1100 


Total 

101 




Average. . . 

1070 

4-7-22 

7 

16 

30 

22 

1640 

809 

1143 


8 

15 

54 

22 

1830 

780 

1107 


9 

16 

84 

22 

1750 

797 

1149 


Total 

47 




Average. . . 

1133 


51 For the average velocity of pulsation equal to 1090 ft. and 
for 4.88 pulsations per second, the pressure wave length as shown 
on the diagrams would be 223 ft. 

52 Since the velocity of the pulsation is independent of the 
velocity of the flowing air and is evidently equal to the velocity 
of sound in air, it seems quite reasonable to conclude that the 
pulsation is a pressure change in the form of a wave front resem¬ 
bling a sound wave of low frequency. It seems also highly probable 
that these pulsations are similar in character to the pulsations set 
up by water hammer in a pipe line, since they also travel with the 
velocity of sound in water. 

53 We gained some additional knowledge of the nature of 
the pulsation by noting its effect on manometers. Where a mano¬ 
meter was used to measure a differential head at a meter, the 
following effects were consistently present: 
















HORACE JUDD AND D. B. PHELEY 


29 


a For pulsationless flow the reading was very constant, the 
only variation being a slight long period surge due to appreciable 
variations in the compressor speed. 


TABLE 4 OBSERVED DATA AT METER 





Readings on Manometer 


No. 

Setting of Line 

Instrument 

Used 

1 

2 

3 

Remarks 




Lt. 

Rt. 

Tot. 

Lt. 

Rt. 

Tot. 

Lt. 

Rt. 

Tot. 


ll 


9"X9" vol. at com- 

Vent. 28" Man. 

12.9 

13.2 

26.1 

12.8 

13.3 

26.1 

12.7 

13.3 

26.0 

Temp 2 

2 

> 

pressor 

“ Foxboro 

cha 

rt 

19. 



19. 



19. 

= 86.5° 

3 



indicator card 










R.p.m. 

4 

< 



Film No. 255 

at 

Ia2 








= 288 

5 1 

> 

9"X9" vol. at comp. 

Vent. Foxboro 



21.8 



21.8 



21.8 


7 I 


9"X1S" vol. midway 

“ 28 M. 

13.5 

13.8 

27.3 

13.3 

13.8 

27.1 

13.2 

13.5 

26.7 


10 1 


9"X9" vol. at comp. 

< ( it 

11.7 

12.1 

23.8 

11.7 

12.2 

23.9 

11.7 

12.2 

23.9 


U 


9"X27" vol. midway 

1 “ Foxboro 



20.6 



20.6 



20.6 

Temp. 

14 


9"X9" vol. at comp. 

it it 



20.0 



20.0 



20.0 

= 99° 

i5 


9"X36" vol. midway 

“ 28" M. 

12.8 

13.2 

26.0 

12.7 

13.1 

25.8 

12.7 

13.2 

25.9 


18 i 


9"X9" vol. at comp. 

ii it 

12.9 

12.2 

25.1 

12.6 

13.3 

25.9 

12.1 

12.8 

24.9 

(Runs 

19 


9"X45" vol. midway 

“ Foxboro 



19.8 



19.8 



19.8 

made 

22 


9"X9" vol. at comp. 

“ 28" M. 

11.9 

12.6 

24.5 

11.9 

12.4 

24.3 

12.0 

12.6 

24.6 

7-20-21) 

23 


9"X54" vol. midway 

“ Foxboro 



18.6 



18.6 



18.6 


26 


9"X45"vol. at comp. 

“ Foxboro 



21.0 



21.0 



21.0 


27 


9"X54" vol. midway 

“ 28" Man. 

12.0 

12.6 

24.6 

12.0 

12.7 

24.7 

12.0 

12.7 

24.7 


2 

9"X45" vol. at comp 

"3 §3 

9.8 

10.6 

20.4 

9.8 

10.5 

20.3 

9.8 

10.4 

20.2 


5 

9"X18"vol. “ “ 

o .2 ■£ 

z. 

<D U S 

14.1 

14.4 

28.5 

14.1 

14.3 

28.4 

14.2 

14.3 

28.5 

R.p.m. 

8 

9"X27"vol. “ “ 

S £ § 

12.4 

12.9 

25.3 

12.5 

12.9 

25.4 

12.6 

13.0 

25.6 

= 288 

11 

9"X36" vol. “ “ 

• pH _a 

03 

*3 on c 

11.3 

11.9 

23.2 

11.2 

11.7 

22.9 

11.2 

11.8 

23.0 

(Runs 

14 

9"X54" vol. “ “ 

■Z R 

a _ 

8.8 

9.7 

18.5 

9.1 

9.6 

18.7 

9.0 

9.7 

18.7 

made 

17 

Line Clear 

(D rC O 

15.8 

17.0 

32.8 

15.9 

17.0 

32.9 

15.7 

17.0 

32.7 

7-21-21) 

22 

Pulsationless 

* &E 

4.1 

5.1 

9.2 

4.1 

5.1 

9.2 

4.1 

5.1 

9.2 


20 

Pulsating — O.L. 


14.0 

13.2 

27.2 

14.0 

13.2 

27.2 

14.0 

12.9 

26.9 

R.p.m. 

22 

Pulsationless 

vO <3 +3 % 

QZ g 

11.7 

11.4 

23.1 

11.9 

11.6 

23.5 

12.0 

11.7 

23.7 

= 291 

29 

1-1" Orifice 

CO £ £ O 

co S ^ c 

12.6 

12.1 

24.7 

12.7 

12.2 

24.9 

12.7 

12.1 

24.8 


30 

31 

2- 1" Orifices 

3- 1" 

t-< a> 5 

O O CO j- 
^ ya <N M 

11.8 

12.2 

11.4 

11.5 

23.2 

23.7 

12.5 

12.2 

11.7 

11.5 

24.2 

23.7 

11.5 

12.2 

12.5 

11.7 

24.0 

23.9 

T 2 =95° 

(Runs 

32 

4-1" 

u ^3 <o 

O -u v 

12.3 

11.6 

23.9 

12.1 

11.5 

23.6 

11.6 

11.6 

23.2 

made 

33 

5-1" 

% i 

12.0 

11.5 

23.5 

12.0 

11.0 

23.0 

12.0 

11.5 

23.5 

8-5-21) 

2 

1" Orifice 


13.9 

13.3 

27.2 

14.0 

13.4 

27.4 

13.8 

13.3 

27.1 

R.p.m. 

3 

4 

2 8 n it 

3 35 

2 5// «« 

3 2 

"S .2 -g 

^ a n a 

eo <u P o 

12.3 

12.2 

12.0 

12.0 

24.3 

24.2 

12.5 

12.3 

12.2 

12.1 

24.7 

24.9 

12.4 

12.2 

12.1 

12.5 

24.5 

24.7 

= 291 
(Runs 

5 

2 2* «« 

CO C > fl 
* ca 

12.3 

12.0 

24.3 

12.3 

12.0 

24.3 

12.3 

12.0 

24.3 

made 

6 

19» it 

■£ 00 c 

O « 

12.4 

12.1 

25.5 

12.7 

12.3 

25.0 

12.7 

12.3 

25.0 

8-6-22) 


b For pulsating flow this surge was magnified greatly, 
c For pulsating flow there is also a rapid vibration of the 
water column corresponding to the pulsations and depending in 
amplitude upon the local conditions at the manometer. 



































































, 30 EFFECT OF PULSATIONS ON FLOW OF GASES 

d The most significant characteristic of the readings for 
pulsating flow was the large increase over that for pulsationless 
flow. This increase was present for every type of manometer, 
meter and gage tried. It varied from a few per cent to several 
hundred per cent under extreme conditions. 

THE ELIMINATION OF THE PULSATION 

54 The problem of the elimination of the pulsation, or of the 
effects due to the pulsation, suggested two methods of attack: (1) 



Fig. 16 Vertical Tank of 200 cu. ft. Capacity as Quieting Chamber — 
Similar to Air Chamber on Pump; 4.9 Pulsations per Sec. 

Distances below compressor: (o) 50 ft.; (6) 117 ft. 


modification of the existing metering devices so that the recorded 
flow would be unaffected whether the flow be steady or in pulsa¬ 
tions ; and (2) the use of devices which would correct or eliminate 
the pulsations before the flowing fluid reached the meter. 

55 The first of these suggested schemes was taken up to some 
extent in the study of the modification of manometer connection. 
The second suggestion, that of pulsation elimination, received the 
















HORACE JUDD AND D. B. PHELEY 


31 


major part of our attention. Of the five quieting devices used, 
the pulsating bag and the revolving fan operated by the air flow 
were studied by means of the photopulsometer. The use of 
throttling devices, the insertion of tanks, volumes or equalizing 
chambers in the line and a combination of the two devices, form¬ 
ing the so-called “ muffler,” comprise the remaining three quieting 
and eliminating devices. These five schemes, it is believed, cover 
nearly all, if not all, of the practical schemes which might be used 
for this purpose. 



Fig. 17 Showing Quieting Effect of Throttling by Means of an Orifice 

(a) 80 ft. below compressor, maximum pulsation in line. (6) 10 ft. below throttling orifice, pulsa¬ 
tion destroyed, (c) 4 ft. above interrupter, 3.5 pulsations per sec. 

56 The tabulated results which follow include the average 
observed data and the percentage of error as figured from these 
average data. The average observed data are the averages of 
three simultaneous readings taken for all manometer readings. 
Tables 4 and 5 are observed-data sheets. In most instances where 
any change in line setting was made a pulsation-flow run was fol¬ 
lowed immediately by a pulsationless-flow run so as to eliminate 
the error due to possible change in temperature. In the few cases 
during the first of the experimentation where this was not done, 
proper corrections were made later for the temperature effect. 





32 


EFFECT OF PULSATIONS ON FLOW OF GASES 


The term “ percentage of error ” for any meter means the percent¬ 
age by which the indicated velocity of flow with pulsations differs 
from the velocity of flow for quiet or pulsationless flow, both read- 

TABLE 5 OBSERVED DATA AT ORIFICE HEAD 


Run 

Orifice-head reading 

Hydrometer 

Instrument or 

Remarks 






No. 

1 

2 

3 

Dry temp. 

Wet temp. 

line setting 


1 

0.911 

0.914 

0.911 

79.0 

70.0 

S ‘S 1? 

o o 5 


2 

0.929 

0.913 

0.916 

78.6 

69.8 

(3 


3 

0.909 

0.917 

0.916 

78.9 

70.0 ' 

<n >3 


4 

0.915 

0.909 

0.900 

79.3 

70.1 

Vol 

the 

ga 


5 

0.911 

0.903 

0.905 

80.5 

70.6 

l-H S® 

Bar. = 29.047 

7 

10 

0.917 

0.920 

0.890 

0.916 

0.877 

0.914 

80.4 

81.1 

70.6 

70.0 

. 'o & 

Z co X 

Zero of 

11 

0.897 

0.892 

0.890 

81.1 

70.1 

. a. fi ^ 

orifice-head 

14 

0.915 

0.910 

0.891 

81.2 

70.0 

rt S 

O O M 

gage 

15 

0.878 

0.875 

0.881 

81.0 

69.8 

CG o 03 .G 

= 0.003 in. 

18 

0.905 

0.903 

0.887 

82.1 

67.7 

C 3 ° " 

.2 ~ ■ S3 <u 

(Runs 

19 

22 

0.902 

0.895 

0.898 

0.887 

0.901 

0.896 

82.6 

82.8 

67.8 

67.7 

Pulsat 

next 

to No 
— alter 

manomi 

made 

7-20-21) 

23 

0.900 

0.895 

0.884 

83.5 

68.0 

26 

0.915 

0.907 

0.894 

83.3 

67.6 

<N u u 

X O <D 


27 

0.905 

0.913 

0.910 

84.0 

67.9 

& O 4) 03 

05 £ S si 


2 

0.905 

0.906 

0.908 

74.3 

66.5 



5 

0.895 

0.904 

0.898 

76.3 

66.5 


Bar = 29.195 

8 

0.900 

0.893 

0.890 

77.0 

66.6 



11 

0.881 

0.890 

0.903 

77.1 

66.6 


Zero = 0.004 in. 

14 

0.880 

0.882 

0.896 

77.9 

66.8 


(Runs 

17 

0.911 

0.910 

0.910 

78.6 

66.7 

Open line 

made 

22 

0.894 

0.906 

0.911 

79.3 

68.1 

pulsationless 

7-21-21) 

20 

0.898 

0.902 

0.901 

79.3 

70.1 

Open line 

Bar. = 29.051 

22 

0.910 

0.906 

0.913 

79.6 

71.2 

pulsationless 


29 

0.913 

0.914 

0.913 

80.0 

70.0 



30 

0.895 

0.920 

0.911 

80.8 

70.5 


Zero = 0.006 in. 

31 

0.915 

0.910 

0.910 

80.5 

69.1 



32 

0.913 

0.917 

0.906 

80.9 

69.8 


(Runs made 

33 

0.886 

0.890 

0.882 

81.2 

71.0 


8-5-21) 

2 

0.910 

0.902 

0.908 

72.5 

63.5 

1 in. 


3 

0.916 

0.920 

0.919 

73.5 

69.5 

If in. 

Bar. = 28.98 

4 

0.915 

0.920 

0.930 

74.0 

70.0 

If m. 

5 

0.925 

0.928 

0.930 

— 

— 

If in. 

(Runs made 

6 

0.930 

0.945 

0.940 

75.0 

70.5 

12 in. 

8-6-21) 


ings taken on the same manometer, or indicating device and with 
a constant quantity of air flowing under the same conditions. The 
condition for constant flow was assured by maintaining at all times 






































HORACE JUDD AND D. B. PHELEY 


33 



Fig. 18 Showing Quieting Effect of 3-in. Revolving Fans Driven by 
Current of Air at Velocity of 22 Ft. per Sec. 

(а) 54 ft. below compressor, pulsation slightly throttled; maximum error due to pulsation, 
68 per cent; 4.5 pulsations per sec. 

(б) Same as (a) but at 80 ft. below compressor. 

(c) 54 ft. below compressor, 6 ft. above fan section; maximum error due to pulsation, 
68 per cent; 4.5 pulsations per Sec. 

(d) 20 ft. below fan section acting as quieting unit; error reduced from 68 per cent to 27 
per cent; 4.5 pulsations per sec. 







34 


EFFECT OF PULSATIONS ON FLOW OF GASES 


a static head of 0.9 in. of water at the orifice head, where special 
care was taken to secure pulsationless-flow conditions. 

Error in Per Cent = (VP^K- 1)100 

where P 2 = corrected manometer reading for pulsating flow 

P x = corrected manometer reading for pulsationless flow. 



Fig. 19 Showing Quieting Effect of Pulsating Bag 

(o) 54 ft. below compressor; maximum pulsation in line. 

(b) 54 ft. below compressor; pulsating bag attached to quiet pulsations. 

(c) 88 ft. below compressor; shows slight quieting effect of the 12-in. volume. 

(d) 117 ft. below compressor; shows complete quieting effect of the 24-in. volume. 

The error in velocity varies as the square root of the error in head 
reading. The manometer readings at the meter were corrected 
to a standard orifice head reading of 0.9 in., by direct proportion. 

57 Modification of Manometer Connections at the Meter . 
The first attempt to reduce the error of pulsation by this means 









HORACE JUDD AND D. B. PHELEY 


35 


was by throttling the manometer connections. These connections 
between the meter in the line and the manometer indicating the 
head readings were made of heavy rubber tubing having an inside 
diameter of ^ in. It has long been the practice to quiet the swing¬ 
ing of a pressure-gage hand by throttling the gage connections. 
Following out this idea, a series of “ orifice plugs/’ see Fig. 4, were 
made by drilling holes of known size in small pieces of brass rod. 


SIMULTANEOUS INDICATOR DIAGRAMS 

■SHOWING RELATION OF PRESSURE CONDITIONS ]N 
COMPRESSOR CYLINDER <$, PIPE LINE. 



"V 


* A 

DIAGRAMS FROM 
COMPRESSOR. CTL. 


DIRECT STATIC CONNECTION 
TO PIPE 5* SPRING 




N32 


NOV. 19,1921 


N23 


NOV. lL 1921 


CONNECTED TO VELOCITY TIP 1 | 
OF PITOT TUBE 
____ 5* SPRINQ 


* 


B 

DIAGRAMS FROM 


STATIC CONNECTION 
■S’*' SPRING 



PIPE LINE 70 
FT FROM COM ¬ 
PRESSOR . 


y 


Fig. 20 Simultaneous Indicator Diagrams 


These plugs were inserted in the rubber manometer tubes both for 
the vertical U-tube water manometer and also for the Foxboro 
differential mercury gage. 

58 Fig. 23 gives the average error for both these gages for 
maximum pulsation while using the venturi meter. The curve 
shows that throttling has no appreciable effect in reducing the error 




























36 


EFFECT OF PULSATIONS ON FLOW OF GASES 


until the opening has been reduced to less than 0.07 in. diameter, 
and that even for an obstruction so small as nearly to close the 
opening the percentage of error is not reduced to within practical 
limits. The Foxboro gage showed the same characteristic in re¬ 
gard to the effect of throttling, but gave an error about 60 per cent 
as large as that for the water manometer. In either case in order 
to reduce the error to 50 per cent of the maximum it would be 
necessary to use an orifice of 0.02 in. diameter, or the diameter of 
a No. 76 drill, clearly a ridiculous size. The surge, or pulsation, 
of the water column was completely destroyed, so that the effect 
is quite analogous to that of the steam gage when throttled. This 



Fig. 21 Analysis of Indicator Diagrams 


indicates that while throttling a pressure gage does not affect its 
reading, it has no beneficial effect in reducing the error due to 
pulsation. That such an error might exist was pointed out by 
Mayo 1 in 1905, and the futility of throttling manometer connec¬ 
tions to reduce the pulsation is also mentioned by Westcott 2 in 1922. 

59 The efficient quieting effect of volumes when used in the 
test line suggested the possibility that small volumes inserted in 
the tubes leading to the manometers might serve to reduce the 
pulsation before the meter was reached. 

1 Trans. Am.Soc.C.E., vol. 54, 1905, Part D, p. 502, Mayo. 

2 Measurement of Gas and Liquids by Orifice Meters, 1922, p. 143, 
H. P. Westcott. 


























































































































HORACE JUDD AND D. B. PHELEY 


37 


60 Our first observations as to the possible effect of a volume 
in the manometer line were made by a comparison of the readings 
of the two manometers (the 6-in. inclined one-leg reservoir oil 
manometer and the 28-in. vertical U-tube water manometer) when 
used interchangeably. These two manometers when used to measure 
the pulsationless flow would agree exactly. When used for pulsat¬ 
ing flow the two would not always agree, although the amount of 
difference between them was difficult to determine. 

61 Several tests were made using the orifice meter and the 
6-in. inclined gage with volumes of different sizes in one or both of 
the manometer connections. The results of these tests show that 



Fig. 22 Analysis of Indicator Diagrams 


the use of volumes in the manometer connections does not give so 
favorable results as the method of throttling. There is only about 
15 per cent reduction in the error for the 70 per cent orifice meter. 

62 It was thought, also, that the point of attachment of 
the manometer connection might have some influence on the error 
due to pulsation. With the orifice meter comparisons were made 
with the manometer connected (1) close to the orifice and (2) at 
a distance of one pipe diameter above the orifice and at points be¬ 
low the orifice ranging from -J diameter to 19 diameters. 

63 Tests made show that for all orifices including the 80 
per cent orifice the error at the standard points of connection is 
greater than that for points near the orifice which averages 96.3 

















































































38 


EFFECT OF PULSATIONS ON FLOW OF GASES 


per cent of the error at the standard points of connection. For 
points farther distant from the orifice there is a tendency for the 
error first to increase and then to decrease as the 19 diameters 
point is approaching, in all covering a total range of 20 per cent 
error. 

64 Effect of Type of Manometer Used. The error in measur¬ 
ing pulsating flow seemed to depend to some degree upon the type 


TABLE 6 MAXIMUM ERROR FOR VENTURI, FLANGE NOZZLE, AND 

PITOT METERS 


Kind of meter 

Error, per cent, average 

Venturi meter. 

82.0 

l|-in. flange nozzle meter. 

76.5 

lj-in. flange nozzle meter. 

94.3 

2-in. flange nozzle meter. 

142.0 

li-in. flange nozzle meter. 

199.0 

No. 1 pitot-tube meter. 

137.0 

No. 2 pitot-tube meter. 

103.0 


of manometer used to register the head, even if all other conditions 
of the line and meter were identical. 

65 It may be stated that all manometers properly graduated 
will give the same head reading for pulsationless flow. But when 


TABLE 7 MAXIMUM ERROR FOR ORIFICE METER 


Size of orifice, 
per cent 

Error, per cent, average 
(from curve) 

33 

15.0 

40 

25.0 

50 

47.5 

60 

81.0 

70 

127.0 

80 

185.0 

90 

285.0 


the flow is pulsating, the ratio of its reading to the true reading will 
differ somewhat according to the variations mentioned above. A 
mercury manometer will probably show an error less than that of 
a water manometer and the latter less than one using mineral oil. 
A manometer with small tubes is likely to read higher than one 
with a larger set of tubes, but this is merely a tendency. If the 

























HORACE JUDD AND D. B. PHELEY 


39 


tubes are too small the capillary effect can be noted; and if they 
are too large, or if they end in a reservoir, the doubtful effect due 
to a “ volume ” will be introduced. The inclined leg of a manom¬ 
eter under some conditions may even cause less “ surge ” effect. 
The presence of a check value or damping device between the two 
manometer legs or chambers, or a float to actuate the recording 


TABLE 8 COMPARISON OF METERS 


Size, per cent 

Error, per cent, average 


Orifice meter 

Flange nozzle meter 

37.5 

20.0 

76.5 

50.0 

47.5 

94.0 

66.7 

112.5 

142.0 

83.3 

207.5 

199.0 


Orifice meter 

Venturi meter 

33.0 

15.0 

82.0 


arm may reduce the error, as is seen in the case of the Foxboro 
gage. 

66 Maximum Percentage of Error Produced by Pulsation. 
For our installation the maximum error for the meters was as given 
in Tables 6 to 9, inclusive. The results show that the less the 


TABLE 9 RESTORATION OF PRESSURE AFTER PASSING METER 1 


Type of meter 

Maximum error, 
per cent 

Restoration of pressure, 
per cent 

Venturi meter. 

82.0 

80.0 

33% orifice meter. 

15.0 

11.5 

40% orifice meter. 

25.0 

19.0 

50% orifice meter. 

47.0 

28.0 

60% orifice meter. 

81.0 

38.0 

70% orifice meter. 

127.0 

48.0 

80% orifice meter. 

185.0 

61.0 

90% orifice meter. 

285.0 

77.0 


obstruction to the flow of the air, the greater the percentage of 
error due to pulsation; also, the greater the restoration of pressure 
after passing the meter, the greater will be the error. The reason 

1 Trans. Am.Soc.M.E., vol. 38, 1916, p. 362, 264: Water Flow through 
Pipe Orifices, H. Judd. 






























40 


EFFECT OF PULSATIONS ON FLOW OF GASES 


for this relation appears to be that, since the pulsation is a form 
of pressure energy, that type of meter unit which in itself most 
completely dissipates the pulsation energy will show the least 
percentage of error. 

67 Distribution oj Pulsation as Shown by Traverse. The 
pipe was traversed by both types of pitot tubes for maximum 



020 0.16 0.12 0.08 0.04 0 

Diameter of Throttling Orifices in Inches 


Fig. 23 Effect of Throttling Manometer Connections — for Venturi 

Meter 


pulsation conditions. The results are shown in Fig. 24. The 
curves of this figure show by both traverses that error due to the 
pulsating flow is least at the center of the pipe. There is a slight 
tendency, as shown by the curves, for the point of minimum error 



CENTER 

Diameter of Pipe,Inches 

Fig. 24 Distribution of Pulsation Across the Diameter of the Pipe 


to be located a little to one side of the center of the pipe. It is not 
known just how much -the pitot tubes themselves are influenced by 
their approach to the wall of the pipe. 

68 Quieting Effect of a Revolving Fan Section (see Fig. 9, 
No. 7). The effect of a revolving fan section when placed in the 
pipe line is shown by Fig. 18. The revolving fan apparently has 




















































HORACE JUDD AND D. B. PHELEY 


41 


some merit as a quieting device, but is of questionable practical 
value. 

69 Effect of the Pulsating Bag as a Quieting Device , Fig. 6, 
is shown by Fig. 19. It is felt that the special'design of such a 
device would be needed to cover the requirement of each individual 
installation in order to correct or eliminate the pulsating error. 

70 Elimination of Pulsation by Throttling. The experiments 
carried on with the various devices for eliminating or modifying 


£ 






























































L 
























\ 












r 












t 












x 





TYPE OF MUFFLE 
8IN.PIPE SECTIC 
POWELL AUTO 

R. SYM 

BOL. 

> 

| 

\ 





N —. c 

. i 






JUDD FUNNEL -* 

NEW FllNNFl - -—-a 


V 












\ 













K 


























o 


A 



A 










0 Z 4 6 8 10 12 

Drop in Pressure Through Muffler,In,of Mercury 

Fig. 26 Effect of Mufflers for Quieting Pulsation — Used with Venturi 

Meter 


the pulsation led to the conclusion that the solution of the problem 
depended entirely on the absorption of the energy of the pulsation 
propagated as a pressure wave closely resembling a sound wave of 
low frequency. Whatever the device used, its value in killing the 
pulsation will be measured by its ability to absorb, or dissipate, 
this energy of pulsation. 

71 The first attempt made to quiet the pulsation was by 
means of throttling either by valve or by orifice. The loss of pres- 










































42 


EFFECT OF PULSATIONS ON FLOW OF GASES 


sure during passage through the valve or obstruction in the line 
was the eliminating factor. 

72 The general effect of throttling is to reduce the error 
rapidly by means of a pressure drop up to 4 in. of mercury. The 
use of a greater pressure drop causes the error to be reduced more 
gradually. The manner of throttling is immaterial whether by 
gate or globe valve or by an orifice. 

73 The general characteristics are summarized in Table 10. 
This table shows that a drop in pressure of 4 in. by throttling is 
needed to make an appreciable reduction in the error; and a drop 
of 6 in. or 3 lb. per sq. in. is necessary to bring the error within 


TABLE 10 ELIMINATION OF THE PULSATION ERROR BY THROTTLING 


Kind of meter used 

Drop in pressure by throttling, inches of mercury 

0 

2 

4 

9 

12 

Error, per cent 

Venturi. 

82.0 

26.0 

10.0 

5.0 

2.5 

33% orifice. 

10.0 

2.0 

0.0 

0.0 

0.0 

50% orifice. 

58.0 

17.0 

7.0 

4.0 

2.0 

70% orifice. 

145.0 

50.0 

18.0 

9.0 

4.0 

80% orifice. 

175.0 

67.0 

25.0 

12.0 

4.0 

90% orifice. 

315.0 

118.0 

22.0 

-5.0 

18.0 

l$-in. flange nozzle. 

44.0 

18.0 

8.0 

3.5 

1.0 

l§-in. flange nozzle. 

83.0 

28.0 

10.0 

5.0 

1.0 

2-in. flange nozzle. 

156.0 

50.0 

16.0 

6.0 

1.0 

2|-in. flange nozzle. 

340.0 

97.0 

31.0 

7.5 

1.0 

Pitot No. 1. 

160.0 

50.0 

20.0 

-7.0 

2.5 

Pitot No. 2. 

140.0 

81.0 

5.0 

0.0 

3.5 


practical limits. In most cases the error is not reducible below 
1 to 3 per cent, even with a sacrifice of a drop of 12 in. mercury. 

74 Elimination of Pulsation by the Use of Volumes. Tanks, 
or volume capacities, or “ volumes,” as we have chosen to call them, 
were used in the line for the purpose of quieting the pulsation. 
These volumes were inserted in the line so that the direction of 
flow through them was along the axis of the volume. The connec¬ 
tions were made,by means of pipe flanges; and later orifices were 
inserted in these flanges at the entrance and exit of each volume. 
This produced an abrupt entrance into and an abrupt exit out of 
the volumes, which in itself would tend to cause a loss of energy; 
and hence would probably contribute toward the reduction of the 
energy imparted to the pulsation. These volumes were all cylin- 






























HORACE JUDD AND D. B. PHELEY 


43 


drical in shape and with the exception of the 8-in. and the 48-in. 
volumes were made of thin sheet metal, No. 24 gage. 

75 The quieting effect due to the use of volumes is shown by 
the curve sheet in Fig. 25. The dotted curve is drawn in as a 
representative average curve for both venturi and orifice meters 
where volumes, alone, are used. 

76 The 24-in. volume in our test line, situated below the 
meter, had a capacity of 29 cu. ft., and was plainly one of ample 
size to convert the pulsating flow into pulsationless flow when the 
air reached the line leading to the orifice head. It is evident from 
these results that a volume is also a practical means of eliminating 



Fig. 25 Percentage of Error for Venturi and Orifice Meters — Pulsation 
Quieted by Volumes 

the pulsation. The chief question is, whether in large installations 
volumes of sufficient size would be of practical use. 

77 Effect of Varying the Shape of Volume was also studied. 
In a general way a volume is probably more efficient when it is of 
relatively large diameter. 

78 Elimination of Pulsation by Combining Throttling with 
Volumes. Since the pulsation could be nearly if not quite elimi¬ 
nated either by the use of throttling devices or by the use of volumes 
alone, the natural conclusion was that some combination of the two 
schemes might be discovered which would give satisfactory results 
without the objectionable large pressure drop or the excessive size 
of the volume. A series of runs was made, while the various 
volumes were in the line, where orifices of various sizes were placed 




































44 


EFFECT OF PULSATIONS ON FLOW OF GASES 


at the entrance and exit of the volumes. The venturi and the ori¬ 
fice meters were used in these tests. It was found that it was 
possible with a volume of several cubic feet, combined with a pres¬ 
sure drop of about two inches of mercury, to reduce the error to a 
small figure, even for a meter having a large maximum error. 

79 The Muffler as a Quieting Device. Following the experi¬ 
ments with the volumes and orifices combined as a means of 
eliminating the pulsation, the idea was further developed by the 
combination of a volume with several orifices; or in other words, 



Static Pressure in Line, Inches of Water 

Fig. 27 Effect of Pulsation on Venturi Meter in “ Dead-End ” Line 


the adaptation of the principle of the automobile muffler to the 
problem of pulsating flow. 

80 To study the effects of a muffler a device was constructed 
of 8-in. pipe-flange sections, as in B , Fig. 8. The curve given in 
Fig. 26 is based upon all the results obtained for every type of 
muffler tested. The results for the 8-section muffler were more 
complete and show at the upper limit an error of 81.5 per cent for 
pulsating flow for open pipe. The whole curve shows that the 
effectiveness of any single type of muffler, aside from its value as 
a volume alone, depends entirely upon the amount of throttling 
produced and very little upon the design and arrangement of its 
baffle work. 



































HORACE JUDD AND D. B. PHELEY 


45 


POSSIBILITY OF ADJUSTMENT OF ERRORS 

81 There is a possibility that the error shown by a meter 
when measuring pulsating flow may be so adjusted or so com¬ 
pensated for, that the true quantity passing through the meter may 
be known. This is mentioned as a possibility only, and forms a 
basis for comments on some of the circumstances which would attend 
such an attempt. 

82 There is the first possibility of the integration of the curve, 
obtained by means of the photopulsometer, which is a series of 



Fia. 28 Effect of Pulsation on Orifice Meter in “ Dead-End ” Line 

velocity-time diagrams. The second possibility would be the use 
of a correction factor for the manometer itself. A third possibility 
would be the determination of a pulsating factor by calibration 
under actual running conditions. 

83 Effect Produced by “ Dead-End ” Pulsation. During our 
experiments in connection with the effect of pulsations on the static 
pressure we had noticed indications of a reading on the meter for 
zero velocity in the line. Later a series of tests was made with each 
of the four meters in while the test line was closed at different points 













































46 EFFECT OF PULSATIONS ON FLOW OF GASES 

beyond the meter station. The static pressure, at a point in the 
line 6 ft. above the meter, was maintained the same as during the 
regular line of tests for 0.9 in. static head at the orifice head. This 
static pressure was secured by regulating a by-pass valve in the 
line 18 ft. above the meter (see Fig. 10). The line could also be 
closed at flanges located at 8 ft., 18 ft., 40 ft., and at the orifice 
head, 45 ft. below the meter. For the “ dead-end ” tests most of 
the runs were made with the large tank, T, in the line, and a few 
runs were made with the large tank out of the line. 

84 The effect produced by the “ dead-end ” pulsation is repre¬ 
sented by the flow equivalent to the reading on the meter as com¬ 
pared with the flow under pulsationless-flow conditions. The curves 



Static Pressure in Line, Inches of Water 

Fig. 29 Effect of Pulsation on 1£-in. Flange-Nozzle Meter in “ Dead- 

End ” Line 

shown in Figs. 27-31 show this relation for the four types of meters. 
The standard flow conditions as represented, during the regular 
runs, by the 0.9 in. static head at the orifice head, the static pres¬ 
sure in the line above the meter would read about 9.5 in. of water 
for pulsationless flow and the corresponding static head under pul¬ 
sating flow would range from 9.5 in. to 16 in. of water, according 
to the type of meter used. Generally speaking, as would be ex¬ 
pected, the static pressure in the line read a little higher under 
pulsating flow than under pulsationless flow, in some cases showing 
an increase of 3.5 in. in 10 in. This would be equal to an error of 
16 per cent due to pulsation. 

85 The curves, Figs. 27-31, give, especially, the effect due to 
change in static pressure in the line while the meters are in a 
“ dead-end ” line. For all meters there is an increase in pulsating 
effect as the static end is increased up to 20 in., after which they 
increase more gradually up to 40 in. static pressure, the limit of 
the tests. 



























HOKACE JUDD AND D. B. PHELEY 


47 


86 In most cases there was a tendency toward an increase 
in the false flow reading with increase of distance to point of line 
closure from the meter. In two instances the meter showed a nega¬ 
tive reading. The rapid change in this effect on the meter with 
variation in static pressure, together with the marked variation in 
apparent flow with change in point of line closure from the meter 
makes it exceedingly doubtful whether any reliability could be 
placed on this method of obtaining the pulsation factor for any 
given installation. 

87 Application of Proposed Formula to Pulsating Flow. An 
attempt has been made to test the relation expressed by the follow- 



Sfaiic Pressure in Line,Inches of Wafer 

Fia. 30 Effect of Pulsation on Pitot Tube No. 1 in “Dead-End” Line 

ing formula by means of the “ dead-end ” flow data. This form- 
ula 1 is: P 2 /(Vp;±VD) 2 X 100 = 100 per cent, where P lf P 2 
and D are respectively the corrected manometer readings for pulsa¬ 
tionless flow, pulsating flow, and “ dead-end ” flow. The positive 
value of D has been used since it was considered to be better 
adapted to the data taken. 

88 Fig. 32 shows the relation between the ratio P 2 to 
(VpT ± VZ )) 2 and the point of line closure. The curve in broken 
lines is the average for the total number of results; the full line is 
the average for the few points for the line without the volume, Q. 
For the 8-ft. distance the results are widely scattered and indicate 
1 Measurement of Gas and Liquids by Orifice Meter, H. P. Westcott, 1922. 



































48 


EFFECT OF PULSATIONS ON FLOW OF GASES 


that this distance is too close to the meter. The 18-ft. distance 
gives results showing more uniformity with the average close to 
100 per cent. This would indicate the formula would apply better 
for line closure at 18 ft. The 45-ft. point, though representing the 
end of the duplicate line, with an average ratio falling below 100 
per cent, would indicate less agreement with the formula. The 
volume Q does not make any marked effect, or as much effect as is 
shown by difference in length of line closure from the meter. 

89 The uncertainty as to where the point of closure should 
be made or as to whether a length of line duplicating any given 



Fig. 31 Effect of Pulsation on Pitot Tube No. 2 in “ Dead-End ” Line 

line would give the true pulsating-head factor make it doubtful 
whether the proposed formula could be applied with any assurance 
of a reasonable degree of accuracy. 

CONCLUSIONS 

90 This investigation relating to our special installation is 
summarized as follows: 

A Nature of Pulsations: 

a Pulsations in a pipe line, originating from a reciprocating 
piston, or a similarly disturbing system, consist of sudden changes 
both in the velocity and in the pressure of the fluid. 

b The pressure change is the most apparent and is probably 
the greatest factor in producing errors in metering devices. 
































HORACE JUDD AND D. B. PHELEY 


49 


c The pressure change is in the form of a wave front resem¬ 
bling a traveling sound wave of low frequency. 

d The pressure wave travels in the pipe with the velocity of 
sound. 

e The velocity of the pulsation is independent of the velocity, 
or quantity, of fluid flowing. 

/ Pulsations in air flow are similar to the compression waves 
set up by water hammer. Both travel at the velocity of sound in 
the fluid and are independent of the velocity of flow. 

g The effect of this pulsation on a flow meter is to increase its 
reading, often causing an error of great magnitude. The magnitude 


Ratio = P 2 /(S%~’*■ /IT ) 2 PerCent 



Fig. 32 Effect of Line Closure on Proposed Formula — with “ Dead-End ” 

Pulsations 


of this error depends upon the frequency of pulsation, nominal 
static pressure of the fluid, type of meter used and adjacent fixtures 
in the pipe line. 

h With orifice meters and flange nozzle meters the pulsating 
error increases as the diameter of the orifice, or nozzle, approaches 
the diameter of the pipe. 

i The throttling or modification of the manometer con¬ 
nections to the meter does not appreciably reduce the error. 

j The point of attachment of manometer connection has no 
great effect on the error due to pulsating flow. 

k The pulsation error at the center of the pipe is 35 per cent 
less than that at the wall of the pipe. 




































50 


EFFECT OF PULSATIONS ON FLOW OF GASES 


l A meter on a “ dead-end ” connection will usually show a 
positive error of considerable magnitude. 

m The pulsation must be eliminated or greatly reduced in 
order to have the meter read without objectionable error. 

B Practical Elimination of Pulsations: 

n Because of the high velocity of the pulsation, an excessive 
length of pipe line would be necessary to destroy the pulsation. 

o Throttling is effective but requires a pressure drop of 6 in. 
of mercury to reduce the error to 5 per cent. 

p Abrupt volume enlargements in the pipe line will eliminate 
the error, if of sufficient capacity. A volume capacity of 20 cu. ft. 
is required for an error within 2 per cent. 

q Generally speaking, for the same capacity, a volume of 
relatively large diameter is more effective than one of small 
diameter. 

r No relation was found between the compressor displace¬ 
ment and the capacity of the volume chambers. 

s The combination of throttling with volumes forming the 
“ muffler ” device probably is the most effective device for the 
mechanical elimination of pulsations. 

t The pulsating bag, or diaphragm, and the fan, or revolving 
baffles, are partially successful in eliminating the pulsations, but 
their installation is thought to offer serious practical objections. 

u The effectiveness of any of these quieting devices seems to 
depend upon their ability to dissipate or change the energy of 
pulsation which is effected chiefly through a drop in pressure. 

v The device which will destroy the pulsating energy with 
the least obstruction to the flow of the fluid is the most desirable. 

w The effectiveness of the meter element itself in quieting 
the pulsation depends upon the degree of restoration of the pres¬ 
sure beyond the meter. The greater the percentage of restoration, 
the higher the percentage of error shown for any given type of 
meter. 

C Adjustment of Error of Pulsation: 

x It is probably not feasible to correct any meter by means 
of a correction factor owing to the disturbing effects which may 
arise from slight changes in the installation and running conditions. 
y The experimental establishment of a pulsating correction 


HORACE JUDD AND D. B. PHELEY 


51 


factor and its relation as shown in the proposed formula is not 
considered feasible with our present experimental knowledge of the 
laws of pulsating flow. 

z It seems probable that each installation where pulsating 
flow is present would present its own peculiar problem for which 
an individual study and consideration of the existing conditions 
would be necessary for a satisfactory solution. 


BIBLIOGRAPHY 

Fluid Flow, Fl-22. Turbulent Flow of Fluids, by Research Committee. 
Am.Soc.M.E. 

Trans. Am.Soc.C.E., vol. 47, 1902, pp. 1-369: Experiments on Effect of 
Curvature upon the Flow of Water in Pipes, Williams, Fenkell, and Hubbell. 

Univ. of Wis. Bull. Engng. Series, vol. 8, no. 3, pp. 147-178, 1914: 
Investigation of Flow Through Four-Inch Submerged Orifices and Tubes, 
Leland R. Balch. 

U.S. Bureau Standards. Sci. Paper 278: An Investigation of the Laws 
of Plastic Flow, E. C. Bingham. 

Engineering News, vol. 76, 1916, pp. 825-827: Experiments with Sub¬ 
merged Orifices and Tubes, T. C. Rogers and T. L. Smith. 

Engineering News, vol. 75, pp. 302-304: Lost Head Diagrams for Bends 
in Water Pipe, Ben Moreel. 

Power, vol. 44, 1916, p. 245: Action of Venturimeter with Pulsating 
Flow, L. A. Wilson. 

Engineering Experiment Station, Univ. of Ill., Bull. 96, 1917, p. 48: The 
Effect of Mouthpieces on Flow of Water through a Submerged Short Pipe, 
F. B. Seely. 

Trans. Am.Soc.C.E., vol. 82, 1918, pp. 185-249: Pulsations in Pipe- 
Lines as Shown by Some Recent Tests, H. C. Vensano. 

^Mechanical Engineering, vol. 42, pp. 616-618, 1920: Effect of Fittings 
on Flow of Fluids through Pipe Lines, Dean E. Foster. 

Proc. Royal Soc. (London), series A, vol. 97, pp. 41&-434, 1920: On 
the Conditions at the Boundary of a Fluid in Turbulent Motion, T. E. 
Stanton and others. 

Engineering, vol. Ill, pp. 639-640, 1921: A New Hydraulic Paradox. 
Other References: 

Trans. Am.Soc.C.E., vol. 54, 1905, part D, p. 502: Pulsations Effect 
on Static Gage Readings, Mayo. 

Power, June 12, 1916, p. 854: Measurement of Steam Flow, E. G. Bailey. 

Trans. Am.Soc.M.E., vol. 38, 1916, p. 278: Establishing a Standard 
of Measurement for Natural Gas in Large Quantities, F. P. Fisher. 

Measurement of Gas and Liquids by Orifice Meter, H. P. Westcott, 


1922. 


52 


EFFECT OF PULSATIONS ON FLOW OF GASES 


Report No. 49. National Advisory Committee for Aeronautics, 1920, 
p. 30: Metering Characteristics of Carburetors. 

Technical Notes No. 40, National Advisory Committee for Aeronautics, 
1921, p. 3: Effect of Reversal of Air Flow Upon the Discharge Coefficient 
of Durley Orifices, Marsden Ware. 

Power Plant Engineering, Nov. 1, 1921, p. 1044: Use of Nozzles for 
Measuring Flow, W. Trinks. 

Power, Jan. 17, 1922, p. 91; also June 27, 1922, p. 1024: The Maxim 
Industrial Silencer in the Power Plant. 

Trans. Am.Soc.M.E., vol. 42, 1920, p. 26: Physical Basis of Air- 
Propeller Design, F. W. Caldwell and E. N. Fales. 

The Science of Musical Sounds, p. 78, D. C. Miller. 

Trans. Am.Soc.M.E., vol. 38, 1916, pp. 362-364: Water Flow through 
Pipe Orifices, H. Judd. 


DISCUSSION 

H. N. Packard. We do not agree that the “ pressure change 
... is the greatest factor in producing errors in metering devices.” 
For instance, imagine a compressor cylinder discharging through a 
short length of pipe, in which is mounted a pitot tube, into a large 
volume such as a gasometer. In the pipe section no measurable 
static pressure change during the cylinder discharge can be detected, 
but a very appreciable variation in rate of flow must occur with 
the consequent error of meter reading. This is readily confirmed by 
actual test with the pitot tube. As a further proof of this point, in 
the Thomas meter, which is entirely independent of pressure con¬ 
ditions and indicates only the standard units flowing through it, 
we have errors with heavily pulsating flows. Assuming a pulsating 
flow of sine wave form, the meter error is negligible up to the point 
where the flow at the peak of the wave does not vary more than 30 
per cent from the mean rate. When the wave amplitude is as great 
as the mean flow, giving instantaneous stoppage of flow in each 
cycle, the meter error reaches a maximum of nearly 8 per cent. 
As practically all meter installations are fairly close to the pulsation 
producing piston, we believe the errors are mostly due to actual 
instantaneous flow variations through the metering device. 

We believe that the velocity of transmission of the wave is 
that of sound plus that of the gas velocity, slightly modified by 
the size and shape of the pipe line. We have found a number of 
references in standard works on physics that the velocity of sound 
in air is dependent on the wind velocity as well as the density of 
the air. Do the authors feel that their data can support their state- 


DISCUSSION 


53 


ment? Their maximum test velocity was 27 ft. per sec. compared 
with about 1100 ft. per sec. for sound, and it seemed to us difficult 
to be sure that the experimental error was not as great as this. 

The curves on Fig. 23 would indicate some reduction in mano¬ 
meter error with throttling of connections. Have the authors any 
explanation of this other than possible leaks? We can see no other 
reason for the gain in accuracy. 

The statement is made that at least a 6-in. mercury pressure 
drop is required to reduce pulsations to a practical limit. Do the 
authors consider this a general statement or applicable only to 
their test conditions? It would appear to me to be a function of 
the density of the fluid, its velocity and the pulsation wave form 
(magnitude of pulsation) if made as a general statement. 

We are still of the opinion that there is some relation between 
the piston displacement and volume of a quieting receiver which 
will give good results. Taking the two absurd extremes of a volume 
equal to piston displacement and an infinite volume, in one case we 
know that no effect will be produced and in the other perfect quiet¬ 
ing of pulsations will occur. We believe that the quantity of fluid 
discharged per stroke, the number of strokes per minute and the 
volume and diameter between the source of pulsations and the meter 
determine the pulsation effect at the meter, at least with elastic 
media such as gases. 

On dead-end error tests we believe that there is an actual 
displacement of gas back and forth in the meter, this flow effect 
being due to the elasticity of the gas which is alternately compressed 
and expanded in the dead-end volume. In our own meter the 
dead-end effect does not occur at all except with such large dead¬ 
end volume that the alternate gas flows through it, traveling at 
least seven inches in a reverse direction. This condition has been 
met but once in our commercial experience. Our meters are nor¬ 
mally set vertically with the normal flow vertically upward. At 
zero load a very small amount of heat is still left in the heater to 
maintain control and due to convection current the heated gas rises 
through the exit thermometer and maintains its temperature higher 
than the entrance thermometer sufficiently to give a constant tend¬ 
ency to shut down the meter. With large dead-end volume and 
severe pulsations there is sufficient back flow to overcome the con¬ 
vection currents and carry heated gas from the heater into the 
entrance thermometer, increasing its temperature to approximately 
the same as the exit thermometer. Immediately the control for the 
meter goes to full load under such conditions. 


54 


EFFECT OF PULSATIONS ON FLOW OF GASES 


J. M. Spitzglass. Prior to the advance of Professor Judd’s 
experimental work on pulsating flow there was an idea prevalent 
that the error in the measurement was due mainly to the magnifying 
effect of the differential column, reading the average height and the 
corresponding square root of this average instead of the average 
of the instantaneous square roots which are the equivalent of the 
varying flow. 

With the development of the flow meter, we sought to eliminate 
this error by making the meter respond electrically to the instan¬ 
taneous instead of the average height of the differential column. 
This provision was thought to eliminate the part of the error which 
the authors of the paper designate as the “ effect of the type of 
manometer used.” We soon discovered that there was a much 
larger error due to the “harmonic” effect of the pulsations in the 
flow. Still, in all our observations with reciprocating flow this 
error seldom exceeded 25 per cent under any circumstances. Further¬ 
more, this error could be easily eliminated by moderate restrictions 
in the form of additional orifice plates on either side of the differential 
medium. 

The writer was greatly surprised when he first glanced at the 
tables in the paper to note that the errors in some of the meters 
were as high as 200 per cent and over. The writer does not for a 
moment cast any doubt on the data of the given observations, but 
he has felt from the beginning that there must be something mis¬ 
leading in the algebraic presentation of the results. After reading 
the paper a second and third time, the solution of the riddle 
presented itself very clearly. 

In summarizing the tabular results of the investigation, the 
authors adopted the velocity pressure of the flow as the basis for 
comparing the effect of the pressure pulsations, which, according 
to their own explanations and results, was not in the least a function 
of that velocity pressure. What they actually did was to compare 
a variable quantity, the pressure pulsations, on the basis of another 
and more variable quantity, the velocity pressure of the flow in 
the given meter. It will be observed, therefore, that whenever the 
assumed basis, the velocity pressure of the meter, decreased, the 
apparent percentage of error increased in a corresponding ratio. 

The writer believes that this is the real reason why the per¬ 
centage of error increased when the size of the orifice or the flange 
nozzle was increased. The same reasoning applies and is a sufficient 
explanation for the fact that the percentage error increased in the 


DISCUSSION 


55 


case of the pitot tube at the wall of the pipe, where the velocity 
pressure (the assumed basis) is the lowest. Furthermore, the dead¬ 
end phenomenon shows conclusively that the effect of pulsation is 
not a factor of the velocity pressure of the air. 

As the data and the results of the investigation are exceedingly 
important for the users of the meter on pulsating flow, the writer 
would like to ask the authors to include in the paper a summary 
table, similar to Table 4, giving the actual values of the static 
pressure in the line, the actual velocity pressure, and the difference 
in static pressure between the pulsating and pulsationless flow for 
all meters tested. It can be readily seen that if the difference has a 
value of, say, 5-in. of water, it may form a square-root error of 145 
per cent on a meter whose velocity pressure is only one inch of 
water, while the same 5-in. difference will form an error of only 
5 per cent on a meter whose velocity pressure amounts to 50-in. 
of water; and what is more important, if by means of moderate 
restriction or increased volume the difference is reduced from 5 
to 0.5 in., it will still give an error of 22 per cent in the first case 
and will be entirely insignificant in the second case. To state this 
in another way: The effect of pulsation, according to the writer’s 
understanding of the investigation, is shown to be rather in the 
nature of an additional term than a factor in the algebraic expression 
of the flow for a given meter. 

R. J. S. Pigott. The paper on pulsating flow reports the 
results of research work undertaken for the Special Committee on 
Fluid Meters, of the Society’s Research Committee. 

One point about pulsating flow seems to be coming more strongly 
to the fore; that is, the problem is largely an acoustic one. All the 
data go to show that the variability of the conditions is due to the 
fact that the acoustic conditions in the pipe differ with every in¬ 
stallation, and it is hard to see how pulsating flow can be stopped in 
every case until a study is made of the phenomena from an acoustic 
standpoint. 

Up to the present time we have not developed devices for 
detecting the acoustic variations. We have been working along 
lines of mechanical devices almost wholly, and have never given 
enough attention, as yet, to demonstrating clearly what are the 
acoustic conditions in the pipes. 

One of the earliest problems in the opinion of the members of 
the Fluid Meters Committee was that of either providing correction 


56 


EFFECT OF PULSATIONS ON FLOW OF GASES 


for the effect of pulsating flow upon the indications yielded by the 
flow meter mechanism, or to so reduce the pulsations as to render 
their effect insignificant. The net result of research has definitely 
confirmed the belief that any type of meter operating on a difference 
of head which is proportioned to the square of velocity will register 
high on pulsating flow. The other belief, that it is very difficult, if 
not impossible, to provide suitable correction factors for the readings 
of the meter, is also very largely confirmed. The problem, therefore, 
is mainly reduced to providing commercially practicable means for 
suppressing pulsations to a point where they do not have a marked 
effect in the registration of the meter. 

The experimental work so far carried out has indicated that 
it is feasible to accomplish this end by means of a combination of 
throttling with enlargement of volume. The scope of the experi¬ 
mental work has not been large enough as yet to definitely establish 
the amount of throttling and the -amount of volume enlargement 
required for any particular case and it is probable that the variations 
in velocity and size of lines will render an exact solution for any 
specific case difficult. However, there is a good deal of encourage¬ 
ment to be drawn from the evidence that in all likelihood proper 
relations of the two requirements can be determined to cover a 
considerable variation in pulsation condition. The situation on 
pulsating flow is only one factor of several which have tended to 
reduce the reliance placed upon flow meters for accurate measure¬ 
ments, and it is not generally recognized that the inaccuracies 
found in the commercial operation of flow meters are due almost 
entirely to the conditions under which the flow meter is installed. 
Under proper installation conditions, it can be demonstrated that 
any well designed flow meter can give results with perfectly satis¬ 
factory precision. However, in the great majority of installations 
insufficient attention is given to the effect of pulsating flow, eddy 
currents in the lines due to valves, elbows or similar obstructions 
and leakage in the lines, transmitting a pressure difference to the 
meter indicating and recording mechanism. 

The first report of the Fluid Meters Committee was to have 
been produced for the Annual Meeting but the amount of work to 
be done both in editing the report and preparing for printing was 
too much to permit publication at this time. 

This report will cover the matter of installation very fully as 
well as the theory and accuracy of the devices employed. It is to 
be hoped that this report will provide for the designers and users 


DISCUSSION 


57 


of flow meters a complete summary of information available on the 
subject. Hitherto there has been no single source from which 
this information could be obtained and it has been scattered through 
three or four hundred different publications. 

John L. Hodgson . 1 In the opinion of the writer, the results 
obtained from the elaborate researches described in the paper 
might have been very much greater had a careful analysis been 
made beforehand of the ways in which pulsating flows cause errors 
in meters which are based upon the measurement of a differential 
pressure. 

By making such an analysis the writer has found it possible to 
reach wider and more general conclusions than the authors of the 
present paper at the expense of far less experimental work. 

Some of the most important of these conclusions are summa¬ 
rized below. 

A pulsating air flow may be considered to consist of: 

a A “pressure variation” which is transmitted with the 
• velocity of the fluid in the pipe, plus the velocity of the 
sound in the fluid proper to the particular size and rough¬ 
ness of pipe used, and the nearness to the source of 
pulsation of the point where the velocity is measured. 
b A ‘‘velocity variation” during which the whole of the air 
in the pipe is accelerated or retarded. 

The fluid at a point distant from the source of pulsation 
does not however change its velocity until the impulse, 
transmitted with the velocity stated under a, reaches it. 2 

Both these pressure and velocity variations cause errors 3 in 
the meter; but in quite different ways. 

The error due to the pressure variation occurs when the pressure 
pipes leading to the meter have different coefficients of discharge 
for inflows and outflows, and when the capacity in the meter on the 
two sides of the water or mercury column are different. 4 It is then 

1 Eggington House, Beds, England. 

2 The authors state that the velocity of propagation of the impulse is 
that of sound. That may apparently be so in the case of their particular experi¬ 
ments; as the effect of the pipe walls is to retard the speed, and of the moving 
air to increase it. 

3 The above sources of error, and also the effects of “square root” and 
“viscous” damping of the manometer or meter were pointed out in a paper 
by the writer in 1916; see Proc. Inst. C. E., vol. CCIV, p. 134 to 137. 

4 In the case of the photo-pulsometer, shown in Fig. 11, the upstream 


58 


EFFECT OF PULSATIONS ON FLOW OF GASES 


possible to obtain an actual difference of pressure on the two sides 
of the meter by the pressure variation alone and when there is no 
velocity variation at all in the pipe. * 1 

The error due to the pressure variation 2 may easily be brought 
down to a very small amount by using pressure connections which 
have equal coefficients of discharge in both directions, and by keep¬ 
ing the capacities in the meter about equal. 

There remains the error due to velocity variation, which is the 
real source of trouble. 

This causes error because the flow depends upon the mean of 
the square root of the pressure differences across the measuring 
device; whereas the meter reading 3 depends (approximately) 4 
upon the mean of the pressure differences. 

It can be shown by calculation that for certain wave forms 
this “velocity variation” may produce errors of several hundred 
per cent. 

The error due to this cause can be calculated or determined 
by calibration for any particular conditions; but as it varies with 
the rate of flow, and the wave form, and the product of the specific 
volume and the absolute pressure of the fluid, and the loss of pres¬ 
sure in, and the capacity of, the pipe line, it is best reduced to a 
small amount rather than allowed for. 

The only way to reduce it is to smooth out the wave form of 
the “velocity variation” at the metering point. 

This can be done in many ways, the simplest of which (not 
mentioned by the authors) is to insert a capacity and a throttling 

cavity is larger than the downstream cavity, with the result that when a change 
of pressure occurs the pressure will rise and fall most quickly in the downstream 
cavity; thus exaggerating all the readings. Many of the diagrams taken with 
this instrument indicate negative flows (instead of the positive flows which 
must actually have existed) because of this defect. 

1 The “dead end” condition referred to by the authors. 

2 The “pressure change” is wrongly stated by the authors to be “probably 
the greatest factor in producing errors.” The “pressure change” is more rightly 
considered as a “symptom” than a “cause.” 

3 That is, assuming that the meter is adjusted so as to show no appreciable 
error due to the “pressure variation.” 

4 This is only true when the “damping” in the pressure pipes and the 
meter follows the “viscous” law. If it follows the “square-root” law the mean 
meter reading is not the true mean of the pressure differences. This may explain 
the change of manometer error as the pressure pipes are throttled shown in the 
authors’ Fig. 23. The data given in the paper are, however, insufficient to enable 
the point to be settled. 



DISCUSSION 


59 


device between the source of pulsation and the metering point. If 
the meter itself offers sufficient resistance it may form the throttling 
device; if it does not, an additional throttling device may be added. 
The capacity should be placed between the source of pulsation and 
the meter, and the additional throttling device, if any, should be 
placed on the downstream side of the meter. (See Fig. 33.). 

In a paper read before the Midland Institute of Mining, Civil 
and Mechanical Engineers in January 1921, and again in a paper 
read before the Institute of Naval Architects in April 1922, the writer 
showed that, if certain assumptions were made in order to simplify 
the reasoning 1 , it could be proved 2 that the percentage error of a 
meter for any particular wave form depended upon the value of 
the ratio: 

FCL/ZQ 

where F is the frequency with which the wave form repeats 
itself 


REClPROCATlNt 

COMPRESSOR 


BOILER 


2 _r 


CAPACITY 


METER 


THROTTLING ORIFICE 
OR VALVE 


1_J-L 


METER 


p-n 


CAPACITY 


RECIPROCATING 

ENGINE 


THROTTLING ORIFICE 
OR VALVE 

Fig. 33 Location of Capacity .with Respect to Source of Pulsation 

and Meter 


C is the capacity, and 

L is the loss of pressure between the entrance to the capacity 
C and the side of the metering device which is furthest 
from the source of pulsation 

Z is the product of the specific volume of the fluid and its 
absolute pressure 

Q is the rate of weight flow. 

1 Such as that the meter is adjusted so that the “pressure variation” 
causes no error; that the only error is caused by the meter taking the mean of 
the pressure differences across the measuring device, instead of the mean of 
the square root of the pressure differences; that L varies in Q 2 , etc. 

2 For an elementary proof, see the writer’s paper published in the Proc ., 
Inst. Naval Architects, April 1922. 



























60 EFFECT OF PULSATIONS ON FLOW OF GASES 

The writer has developed methods which enable curves con¬ 
necting the values of FCL/ZQ and the per cent error of the meter 
due to the “velocity variation” to be calculated and drawn out, so 
that, given the wave form, and the values of FZQ, the value of CL 



which will reduce the pulsation error to small limits can be immedi¬ 
ately read off. 

Such a curve for a square wave form, Fig. 34, is shown in 
Fig. 35. 1 

Many* interesting results follow from the FCL/ZQ relation, 
among which are: 

1 A large meter error may often be reduced to a negligible 



Fig. 35 Relation of Values of FCL/ZQ and Per Cent of Error 
of Meter 

amount by trebling or quadrupling the value of CL by 
providing for additional throttling and by putting the 
meter further from the source of pulsation so as to secure 
additional capacity. It will be seen that in order to 
reduce the pulsation error, it is equally efficacious to 
1 Compare the authors’ Fig. 26, which is plotted against L only. 















DISCUSSION 


61 


increase C or L. The energy lost is, however, least 
when the pulsation is reduced by increasing C. 

2 If the rate of flow is reduced on account of the compressor 

slowing down (the wave form remaining the same) the 
meter error will be increased, as F and L are reduced, 
and L falls off more rapidly than Q. 

3 Similarly when a steam engine governs, the meter error 

increases as the flow is reduced. The increase in the 
error is greatest when the engine governs on the “cut off ” 
(instead of “on the throttle”), as the wave form is then 
altered for the worse. If there is an appreciable steam 
chest capacity on the engine side of the throttle, the 
pulsation error may actually be reduced when the 
engine governs “on the throttle.” 

4 If the throttling orifice shown in Fig. 33 consists of a 

valve (instead of a fixed orifice) and this valve is shut 
. down (either automatically or by hand) as the flow is 
reduced so that the original L is maintained, the pul¬ 
sation error will remain constant at all flows, if F and Q 
fall off in the same ratio. 

5 It will be seen on reference to Fig. 35 that if the pulsation 

error is large, any small change in the value of FCL/ZQ 
will cause a large change in the pulsation error, whereas 
if the pulsation error is reduced to 1 or 2 per cent there 
may be large variations in the value of FCL/ZQ without 
causing any appreciable change in the overall error of 
the meter. It is therefore far better to reduce the pul¬ 
sation error to a small amount by increasing FCL/ZQ 
than it is to “rate” the meter by actual calibration for 
a large pulsation error. 1 

6 The FCL/ZQ relation explains the author conclusions 

A(h) and B(w), since it shows that the pulsation error 
is large when L is small. 

7 It can be shown that for given values of FLZ and Q the 

amount that the meter reads fast is (roughly) inversely 
proportional to C 2 , or for given values of CLZ and Q 
to F 2 and so on. 

It should be understood that the FCL/ZQ relation, being 
deduced from premises which simplify the actual conditions, does 
1 Compare the authors’ conclusions A(m) and C(x). 


62 


EFFECT OF PULSATIONS ON FLOW OF GASES 


not hold with absolute rigidity in practice, and also that it only 
holds over a limited range of conditions. 1 At the same time it 
serves as a most valuable key to the meaning of what is otherwise 
a mass of unrelated data. 

The writer would say that he disagrees with the authors’ 
conclusions and B(n). 

It will be seen that he is generally in agreement with conclusions 
C(x) and C(z). With regard to the latter he would say that curves 
connecting the values oi CFL/ZQ and the percentage error of the 
meter which he has had calculated out enable his firm (Messrs. 
Geo. Kent of London and Luton, England) to decide on the proper 
value of CL for any particular case at the expenditure of a few 
minutes’ work only. 

In conclusion he would like to congratulate the authors upon 
the scope of their work, and upon the clear way in which they have 
set forth their results. 

The Authors. In reply to Mr. Packard, we can readily see 
that his type of meter would not be greatly affected, if any, by the 
pressure changes, even though the static pressure gage might read 
higher due to the pulsation. We would also conclude from our 
investigation that his meter would be less affected by the pulsation 
because the effect on the velocity head seems to show much less 
error than that produced in meters depending on the pressure 
drop readings. 

In regard to the effect produced by the static pulsation we 
have failed to convey the proper meaning. The change or effect 
on static pressure produced by the pulsation is much greater than 
the effect produced on the velocity head. This pulsation, like 
Sound, seems to be propagated as a pressure wave and the effect 
produced on any measuring device, especially where difference in 
pressure head is used, is much greater than the effect recorded on 
the velocity diagrams from the photo-pulsometer. Hence, the 
conclusion that the “pressure change” was the greatest disturbing 
factor was drawn. This we believe to be borne out in our work. 
By the photo-pulsometer the diagrams with air flow through the 
venturi showed a maximum velocity change of 1| in. = 4.5 in. 
water as taken with the pitot tips which from their construction 
would produce a magnified reading while for the same flow con- 

1 For instance, it does not hold when the rate of flow is so great that the 
loss of pressure, L, no longer follows the square root law. 


DISCUSSION 


63 


ditions, the indicator diagrams giving static pressure fluctuations 
showed a change about 1.2 lb. or say 35-in. water or about eight 
times as great as was shown in the velocity head reading neglecting 
the fact that the instrument gave a magnified reading. 

Furthermore in Fig. 20, the diagrams 1 and 2, section B, show 
a pressure card and a pressure and velocity head card respectively. 
A comparison of the two cards show little or no difference and at 
least indicate no great change, if any, due to the velocity head 
when added to the static head, as taken by a pitot tip attached to 
the indicator cock. 

It seems apparent, therefore, that the pulsation, (assuming its 
propagation as a pressure wave) is transmitted in the pipe by means 
of the air (either flowing or quiet) as a medium; and that with the 
dead-end meter connection the pulsation is surging back and forth 
independent of the air which itself may also have some slight move¬ 
ment back and forth. This transmission of pulsation in the dead¬ 
end line would seem to be similar in this respect to the surge of 
pressure in a water line due to water hammer which is very much 
greater in magnitude as compared with the effect due to velocity. 

In regard to the velocity of the pulsations, the statement 
should be modified to show that the velocity of the pulsation 
included the velocity of the wave and the velocity of the air. For 
the maximum velocity of 27 ft. per sec. the error would be less 
than 3 per cent if we neglect the velocity of the air which of course 
is much less than the actual experimental error. 

The conclusions given in the summary are made with reference 
to the installation which we tested; also reference to the throttling 
effects of a six-inch mercury pressure drop considers our test con¬ 
ditions only, and should be modified much according to Mr. Packard’s 
suggestion. 

In regard to error due to throttling manometer connections, 
we do not believe that there were any leaks, since these manometer 
throttling plugs were made up in sets all of the same material and 
in the same way, and furthermore the data seemed to be consistent. 

Referring to the relation to piston displacement of the volume 
of a quieting cylinder, it is probably true that some relation exists, 
but it seemed to us that it would take such an extended investigation 
to establish anything approaching a law, as to render the solution 
impracticable. 

In the dead-end meter installation, we agree with Mr. Packard 
that there is an actual forward and back flow of the fluid due to 


64 


EFFECT OF PULSATIONS ON FLOW OF GASES 


the elasticity of the gas; but it is also true, we think, that the pul¬ 
sation in the form of the compression wave travels forward in un¬ 
diminished amplitude and returns in more or less diminished ampli¬ 
tude depending on the length, shape, and volume of the dead-end 
connection. 

Mr. Spitzglass states in his discussion that the authors in 
finding the per cent of error due to pulsating flow have compared 
“a variable quantity, the pressure pulsations, on the basis of another 
and more variable quantity, the velocity pressure of the meter.” 

The error due to pulsating flow was based on the velocity, or 
quantity of flow, or its proportional equivalent the square root of 
the pressure difference through the meter element for pulsationless 
flow. For the four types of meters used the velocity head is equal 
to or proportional to the drop, or pressure difference, through the 
meter element. From whatever cause the pulsating flow may have 
been produced it is quite evident that its effect would have to be 
determined from the reading on the meter manometer. 

It appears to us, therefore, that while the pressure pulsation 
seems to be the greatest factor in the error due to pulsating flow 
it is the velocity head reading that is observed on the meter. In 
our opinion it is the velocity-head readings as shown by the meter 
for both conditions of flow that should be compared. In fact we are 
at a loss to know of any other way of establishing the per cent of 
error. 

Mr. Spitzglass also calls attention to the fact that for the 
orifice meter and flange nozzle meter the percentages of error increase 
approximately as the inverse ratio of the velocity heads. The 
reason he assigns is that as the velocity through the meter element 
decreases the effect due to the static pressure pulsations increases; 
and likewise by the same reasoning the apparent increase in per¬ 
centage of error, as the walls of the pipe are reached, can be explained. 
This relation for the orifice and flange-nozzle meters can be noted 
in the following table but it is felt that the data is not sufficient in 
relation to the behavior of pressure pulsation at different points of 
the line to warrant more than a mention of this apparent relation. 

Owing to the limited capacity of the air compressor it was not 
possible to experiment with pulsating air flow under varying static 
pressure conditions. For the dead-end meter connection static 
pressure changes could be noted and it was observed that a rapid 
increase in percentage of error occurred with increase of static 
pressure. Hence in the discussion, where it is stated that a 5-in. 


DISCUSSION 


65 


differential would give 145 per cent error for a flow condition of 
one inch true differential and the same differential of 5 in. would 
give only 5 per cent error for a true differential of 50 in. of water, 
it would be unsafe to predict that the differential would still be 
5 inches for a 50-in. true differential. A flow under 50-in. head 
would necessarily require a much higher static pressure which is 


TABLE 11 FLOW CONDITIONS IN THE TEST LINE 


Meter used 

1 

Static press 

Pulseless 

2 

ure in line abo 
in. water 

Pulsating 

3 

ve meter, 

Difference 

4 

Velocity head 
by meter man., 
in. water 

5 

Maximum 

error, 

Per cent 

6 

Venturi 

10 



9.29 




13.5 

3.5 

30.15 

81.0 

Orifice 

27.7 



22.00 


33% 


32.0 

4.3 

26.35 

9.5 

Orifice 

11.8 



4.10 


50% 


13.4 

1.6 

10.48 

60.0 

Orifice 

9.8 



0.94 


70% 


11.4 

1.6 

4.83 

128.0 

Orifice 

9.4 



0.41 


80% 


10.8 

1.4 

2.93 

167.0 

Orifice 

8.9 



0.0865 


90% 


9.6 

0.7 

1.083 

254.0 

Flange-nozzle 

13.0 



5.59 


If in. 


16.3 

3.3 

11.73 

45.0 

Flange-nozzle 

10.0 



1.64 


1£ in. 


11.4 

1.4 

6.16 

94.0 

Flange-nozzle 

9.3 



0.47 


2 in. 


9.9 

0.6 

2.74 

143.0 

Flange-nozzle 

8.7 



0.121 


in. 


9.4 

0.7 

1.090 

200.0 

Pitot 

8.8 



0.163 


No. 1 


9.2 

0.4 

1.110 

162.0 

Pitot 

8.8 



0.224 


No. 2 


9.6 

0.8 

1.000 

115.0 


likely to result in a differential between pulsationless and pulsating 
flow much greater than the assumed 5 inches and hence the per¬ 
centage of error would be correspondingly increased. 

The authors are glad to comply with Mr. Spitzglass’ request 
to include a table giving in summary a statement of the flow 
conditions in the test line: 

Columns 2 and 3 give the static pressure in the line for pulse¬ 
less and pulsating flow respectively. Column 4 gives the difference 

















66 


EFFECT OF PULSATIONS ON FLOW OF GASES 


in static pressure for pulsating flow over pulseless flow for a velocity 
of flow in the three-inch line of twenty-two feet per second. 

It will be noticed that although the flow conditions were uni¬ 
form for the different meter elements the pulsating effect on the 
static manometer varied, ranging from 0.4 to 4.3 in. of water. 
This variation depended upon the kind of meter element used. 
Those elements which obstructed the pipe most, namely: the 
venturi, the 33-per cent orifice and the l|-in. flange-nozzle, showed 
the greatest effect due to the static pulsation. Where the pipe 
was least obstructed as with the orifice, flange-nozzle, and pitot 
meters the static manometer showed the least effect. Also the 
maximum percentage of error is seen to vary approximately inversely 
as the error shown by the static manometer. 

As pointed out in the paper and as further emphasized by 
Mr. Pigott, the authors believe that very little can be done to 
establish suitable correction factors for meters operating under 
pulsating flow and that the solution of the problem is reached when 
some suitable means is provided which will reduce the pulsations 
to a negligible point. The adaptation of the “muffler” device is 
apparently the most effective mechanical device for reducing the 
pulsations. However, further study and experimentation is necessary 
to establish the proper combination of throttling and volume space 
for static pressures and pulsating conditions approaching those in 
general practice. 

The authors feel greatly honored in having their paper reviewed 
by Mr. John L. Hodgson of England. 

Mr. Hodgson takes exception to certain conclusions in the 
paper, in some cases justly so, and in others due apparently to a 
wrong interpretation of the paper. He points out the importance 
of having equal spaces in the manometer connections of the meter 
and in the case of the photo-pulsometer equal spaces above and 
below the diaphragm. The authors also recognized the importance 
of this and so far as possible all manometer connections were made 
of equal length, although this relation could not be maintained 
while the manometers were in use. Our experiments showed (see 
Fig. 23) that, when the manometer tubes were throttled, a throttle- 
plug, with a diameter of 0.02 in. was necessary to reduce the error 
from 80 to 60 per cent for the venturi meter, with throttling plug 
coefficients the same for flow in either direction and other conditions 
of flow remaining constant. The use of volumes in the manometer 
connections in various combinations and with uniform and similar 


DISCUSSION 


67 


connecting tubes, f in. diameter opening (see “M,” Fig. 4), gave 
no more favorable results than did the throttle plugs. 

With the photo-pulsometer the space below the diaphragm 
was made equal to the space above as were also the connections 
to the searching tubes as shown in the corrected drawing of Fig. 11. 
A partition with a glass shutter extended across the diaphragm 
chamber so that the diaphragm was equidistant from each wall. 
The diagrams showing negative pressure could not therefore be 
caused by unequal capacities. The photo-pulsometer was used 
chiefly as an indicator for illustrating and confirming pulsationless 
flow conditions. 

It is conceivable that the pressure pulsations might be lessened, 
perhaps nearly eliminated, by the use of the proper amount of 
throttling, observing at the same time that equal spaces were pro¬ 
vided at the manometer connections for varying quantities of flow. 
We concluded that it was an extremely doubtful and uncertain 
method, if not wholly dangerous, to rely too fully on such expedients 
for reducing the pulsating error. 

The question raised in regard to the relative effect of the pulsa¬ 
tion on the static pressure is answered, we believe, in the reply to 
Mr. Packard. The authors have designated as static pulsation 
changes all pulsating changes which act in a direction at right 
angles to the stream flow. For the venturi meter, with the usual 
static pressure connections, acting under pulsating flow, the liquid 
in the manometer tubes would steadily rise until a differential 
head was reached equal to more than three times the differential 
head due to pulsationless flow. The column would vibrate through 
a range of \ to f of an inch corresponding in frequency to that 
of the flowing air. This vibration is dffe, in our opinion, to the in 
and out flow through the manometer tubes, and represents the only 
effect on the manometer tubes due to the velocity pulsation, the 
greater part of the manometer reading being due to the static pul¬ 
sations. 

We agree with Mr. Hodgson and Mr. Packard that the velocity 
of propagation of the pulsating wave approaches that of sound in 
the flowing fluid plus the velocity of the flowing air. However, in 
our opinion, as based on our experiments, we are not willing to con¬ 
cede that the pressure pulsation has a less effect than the velocity 
pulsation in meter installations where these pulsations act on 
manometers with static connections at right angles and even with 
the inside of the pipe. From the “dead-end” flow experiments it 


68 


EFFECT OF PULSATIONS ON FLOW OF GASES 


would also seem evident that the pressure pulsation effect is many 
times greater than that due to the velocity pulsation. 

The statement was made by Mr. Hodgson that the simplest 
way of reducing the pulsation by the use of a capacity combined 
with throttling was not mentioned by the authors. In conclusion 
B (s) we have stated that the “muffler” device, a combination of 
capacity, or volume, with throttling is probably “the most effective 
device for the mechanical elimination of pulsations.” The capacity 
or “muffler” was always inserted between the disturbing element 
and the meter. It would not seem advisable in our opinion, to 
insert the throttling device in the line below the meter. It would 
seem better to eliminate the pulsations as far as possible before the 
meter was reached. 

The authors regret that Mr. Hodgson’s paper containing his 
latest investigations involving the development of a formula for 
pulsating flow was not available for examination and study until 
after their paper was written. The grouping of the factors involved 
in pulsating flow in order shown in the formula seems feasible. 
Mr. Hodgson is to be congratulated in being able to reduce the 
results of his researches to a working formula which shows the 
factors involved in their proper relation. We are in full accord with 
the opinion of Mr. Hodgson that the only sure way to meter pul¬ 
sating flow is to reduce the pulsations by means of suitable capacity 
and throttling, and we likewise believe that even the formula pro¬ 
posed, or any similar formula, while serving in a general way cannot 
be too rigidly applied in practice. Each installation will present its 
own peculiar problem. 


APPENDIX A - HISTORICAL 

For at least twenty years it has been noticed that pulsations would compli¬ 
cate and render inaccurate any attempt to measure the flow of fluids by means 
of a meter. In 1902, Williams, Hubbell and Fenkell (*1) investigated the effect 
of turbulent flow produced by flow of water in pipe bends. This was followed 
by further study along the same line in 1916 by Moreel (*2). In 1905 Mayo (*3) 
noticed that the pulsations caused by the impeller of a centrifugal pump raised 
the delivery gage reading 25 per cent higher than the design and running con¬ 
ditions of the pump would warrant. 

In 1916, Rogers and Smith (*4) and in 1917 F. B. Seely (*5) mentioned the 
action of turbulence connected with tests on water-discharge through submerged 
mouthpieces and orifices. E. G. Bailey (*6) also pointed out the serious effect 
of “swirling” in fluid flow. 

F. P. Fisher (*7) found"erratic disturbances in gas mains due to pulsations 
and tried to eliminate them, with partial success, by using a “pulsation equal¬ 
izer” made up of a manifold of small parallel pipes of different lengths. 

L. A. Wilson, (*8) while using a Venturimeter for air flow from a compressor, 
found that the meter would register a flow reading for a closed pipe indicating 
that the pulsations were transmitted to the meter resulting in a reading even 
with no air flow. 

H. P. Westcott (*9) following this lead suggested a formula for correcting 
the effect due to pulsation by making use of the “dead-end” reading on a flow¬ 
meter. 

From 1908 to 1918, studies (*10) of the effect of water hammer in pipe lines 
have been carried on. This is mentioned because of the close relation which, it 
is believed, can be shown to exist between water hammer and pulsations in the 
air line, the difference being that of degree only. 

During the past two years, more definite steps have been taken in an attempt 
toward eliminating, or compensating for, the error due to pulsating flow: 1. As 
reduced by throttling (*11); 2. by the use of tanks (*12); 3. by the use of tanks 
combined with vibrating diaphragms as used by Professor Trinks (*13) for 
measuring the output of air compressors; 4. by the recent introduction of a 
type of silencer (*14) to be applied to exhaust lines in Power Stations. 

*1. Trans. A. S. C. E. Vol. 47, 1902, p. 1-369. “Experiments of Effect 
of Curvature upon the Flow of Water in Pipes.” Williams, Fenkell, and Hubbell. 

*2. Engineering News, Vol. 75, p. 302-304. “Lost Head Diagrams for 
Bends in Water Pipe.” Ben Moreel. 

*3. Trans. A. S. C. E. Vol. 54, 1905, part D, p. 502. “Pulsation Effect 
on Static Gage Reading.” Mayo. 

*4. Engineering News, Vol. 76, 1916, p. 825-827. “Experiments with 
Submerged Orifices and Tubes.” T. C. Rogers and T. L. Smith. 

*5. Engineering Experiment Station, U. of Ill., Bull. 96, 1917, p. 48. 

69 


70 


EFFECT OF PULSATIONS ON FLOW OF GASES 


“The Effect of Mouthpieces on Flow of Water through a Submerged Short 
Pipe.” F. B. Seely. 

*6. Power, June 13, 1916, p. 854. “Measurement of Steam Flow.” 
E. G. Bailey. 

*7. Trans. A. S. M. E. Vol. 38, 1916, p. 278, “Establishing a Standard 
of Measurement for Natural Gas in Large Quantities.” Fisher. 

*8. Power Vol. 44, 1916, p. 425. “Action of Venturimeter with Pulsating 
Flow.” L. A. Wilson. 

*9. “Measurement of Gas and Liquids, by Orifice meter,” p. 143. 
H. P. Westcott. 

*10. Trans. A. S. C. E. Vol. 82,1918, p. 185-249. “Pulsations in Pipe-fines 
as Shown by Some Recent Tests.” H. C. Vensano. 

*11. Report No. 49. National Advisory Committee for Aeronautics. 
1920, p. 30, “Metering Characteristics of Carburetors.” 

*12. Technical Notes No. 40. National Advisory Committee for Aero¬ 
nautics, 1921, p. 3. “Effect of Reversal of Air Flow Upon the Discharge Coeffi¬ 
cient of Durley Orifices.” Marsden Ware. 

*13. Power Plant Engineering. Nov. 1, 1921, p. 1044. “Use of Nozzles 
for Measuring Flow.” W. Trinks. 

*14. Power. Jan. 17, 1922, p. 91. 

Power. June 27, 1922, p. 1024. The Maxim Industrial Silencer in 
the Power Plant. 


APPENDIX B — EXPLANATORY NOTES 

(Page and paragraph numbers refer to corresponding page and paragraph 

numbers in the paper) 

Page 8, Paragraph 11. When the project was first undertaken, the only 
reliable source of power, owing to fuel shortage, was that of natural gas. We, 
therefore, were obliged to limit ourselves at the time to a small air compressor 
driven by a gas engine to furnish the air supply. It was then the intention to 
investigate, also, the effect of pulsations produced in steam and water, but more 
than enough work appeared in connection with air flow to occupy all of the 
available time. 

Page 13, Paragraph 22. This check orifice was placed in the flange near 
the tapered end of the orifice head with a manometer arranged to read the drop 
across it simultaneously with the manometer at the orifice head. All the single 
orifices were checked against the check orifice by comparing the square roots of 
the ratios of the manometer readings. 

Page 14, Paragraph 24. Of the four meter elements used in the study of 
the effects of pulsation, the venturi meter, the orifice meter, and the flange nozzle 
meter depend upon the same fundamental principle, that of pressure drop due to 
change in velocity; the pitot tube depends upon the “impact” principle or the 
conversion of the velocity of flow into its equivalent static head. These four 
types of meters were chosen as being representative of the majority of the 
general class of recording meters of the inferential type. 

Page 21, Paragraph 38. The photo-pulsometer was not available for use 
during the latter half of the investigation. This was regretted in some instances 


APPENDIX B 


71 


especially when studies were being made of the static pressure changes in the 
line and of the probable velocity of the pulsation. However, by means of such 
velocity diagrams as were taken we were able to verify the different velocity 
changes produced by the various modifying causes and especially to check up 
our equipment and to establish the conditions for pulsationless flow at the 
standardized orifice head. 

Page 37, Paragraph 60. The “surge” of the vertical manometer often made 
it necessary to have two observers to get accurate readings, and also a more accu¬ 
rate reading could be made on the inclined manometer than on the vertical 
manometer. One reason assigned for this difference was the presence of consider¬ 
able volume of air in the reservoir at the low pressure end of the inclined 
manometer. 

Page 38, Paragraph 64. The variations possible in manometers in common 
use are as follows: Variation in (1) density of the liquid used, (2) size, shape, 
and position of the manometer tubes, (3) connection between manometer legs, 
(4) recording mechanism. Our experimental knowledge of these different vari¬ 
ations is quite fragmentary but a few tendencies were observed. As previously 
mentioned, the recording head reading on the Foxboro differential recording mer¬ 
cury gage was consistently only 60 % of the head reading on the water mano¬ 
meter. See also Tables 11, 12, 13, 14, 30 Appendix C. 

Page 39, Paragraph 65. It is our opinion, also, that if the connections from 
the pipe to the manometer were short, direct, and as large, or nearly so, as the 
manometer tubes and if the frequency of the pulsation was comparatively low 
the pulsation would.be unusually violent and would cause the liquid in the 
manometer to assume “a wholly indeterminate condition of churned foam” 
as one investigator (*7) describes it. The liquid would attempt to “recover” 
or return to a lower different head between pulsations and the violent fluctuation 
of the column would make accurate reading impossible. In most cases, how¬ 
ever, the manometer connections consist of a series of enlargements and con¬ 
tractions, hence the further addition of special volume units would only tend 
to accentuate this condition. 

If the pulsation is allowed to propagate itself through still air instead of 
through a flowing stream of air, the effect is quite different on the various types 
of manometers. This may be seen by comparing the results shown on Table 27. 
Here four types of manometers were attached to a meter under “no flow” condi¬ 
tions. The pipe line could be closed at different points and the same static pres¬ 
sure was maintained while the compressor was running under the standard 
conditions except that air was by-passed off from the test line 18 feet above the 
meter 

For the Flange Nozzle (Table 30) with pulsationless flow, the reading 
checks closely for the water manometer, the inclined U-tube manometer, and for 
the one-leg inclined manometer. When the pulsations were admitted to the 
“ dead-end” line (for 8 ft. closure) for the same static pressure, 11.8" water 
(increased 2" due to effect of pulsation on the static manometer) the water 
manometer gave a negative reading of .25" (for manometer connections both 
direct and reversed) but there was no agreement among any of the other man¬ 
ometers for the same pulsation conditions and all manometers except the water 
manometer showed a wide variation when the manometer connections were 
reversed. 


72 


EFFECT OF PULSATIONS ON FLOW OF GASES 


Similarly for the 70% orifice meter under the same pulsating conditions, 
while the pulsationless flow readings showed reasonably consistent agreement, 
the action of all of the manometers under the effect of pulsation was very erratic 
with no 'agreement either individually when the connections were reversed or when 
compared with one another. The reason for this disagreement seemed to be due 
entirely to the differences in the size, shape, and position of the manometer 
tubes when in use. The “dead-end” pulsation acted very differently and was 
much more erratic in its effect than the pulsation occurring while the air was 
flowing. The presence of an enlarged reservoir bulb on the low pressure leg 
of the manometer seemed to have less disturbing effect than one connected to 
the high pressure leg. The effect was more pronounced when the bulb was only 
partly filled with liquid owing probably to the increased hydrostatic effect due 
to the increased surface exposed to the pulsation. 

Page 40, Paragraph 67. The increase in per cent of error at the walls of 
the pipe is 30% for Pitot No. 1 and 31 % for Pitot No. 2. No reason can be 
assigned either for this manner of distribution or for the manner of variation of 
these curves in direct opposition to the usual velocity curves as shown by a 
traverse. If Bernouilli’s law holds in this case, for a reduction in velocity near 
the walls of the pipe there would be the corresponding increase in pressure 
Increase in pressure is shown to result in increase in pulsation error but it i s 
thought that the pressure increase would not be sufficient to account for the 
full amount of increase in error indicated by the traverses. See also Table 21. 

Page 41, Paragraph 68. Diagrams a, 6, c, Fig. 18, are taken with the fan 
section removed and the line slightly throttled thus reducing the error due to 
pulsation for open pipe from 80 % to 68 %. The fan-section consisting of three 
closely fitting but freely revolving fans was then placed in the line. The slight 
amount of throttling in addition to the effect of the high speed of the fans 
reduced the error from 80% to 27 %. The fans seem to modify the character 
of the pulsation somewhat as Diagram d shows. There is a distinct dip below 
the zero pressure line. The maximum pulsations range as high if not higher 
than those in Diagram c. No diagrams were available for the point beyond the 
24* quieting volume (Fig. 1, Part Q). In all probability at that point a dia¬ 
gram would have shown pulsationless flow. The per cent of error quoted above 
was computed from other data taken. 

Page 41, Paragraph 69. Comparing the maximum pulsations in the line 
for diagram a, Fig. 19, with the maximum pulsations for diagram b after the 
pulsating bag had been attached shows: 

Average maximum pulsation for diagram a = 0.63 
Average maximum pulsation for diagram b =0.25 
Square root of ratio 25 to 63 = 0.63 • 

Quieting effect due to pulsating bag = 37 % 

Under certain conditions a tank or volume with vibrating sides would, 
no doubt, be of service in reducing the effect of the pulsations. It is felt that 
special design of such a device would be needed to cover the requirement of 
each individual installation in order to correct or eliminate the pulsating error. 

Page 42, Paragraph 72. This rate of change w^as not so rapid when the 
pulsation was artificially produced. See Curves 2 and 3 Fig. 34. See also Tables 
17, 18, 19, 20, 21, Figs. 34, 35, 36, 37. 


APPENDIX B 


73 


For the 90% orifice meter, conditions were such as to produce a negative 
error after the drop in pressure exceeded 5 inches. A similar case was observed 
for the pitotmeter No. 1 and the same phenomenon was also noted in a test 
with the same pitotmeter made earlier but not included in these data. As 
mentioned in the discussion under Effect of Type of Manometer Used for the 
action of the meters under “dead-end” flow, it is believed that certain con¬ 
ditions may arise whereby the effect of the pulsation is as if there were an 
instantaneously negative flow of air which might cause an apparent nega¬ 
tive reading on the meter. The occurrence although not easily accounted for 
cannot be accidental for the instances referred to occurred during tests taken 
at intervals several months apart. It is possible that the partial restoration 
of pressure after leaving the orifice meter with the large orifice may be a con¬ 
tributing cause for the occurrence of the negative error and the subsequent 
increase in error with increase of drop in pressure. 

Page 43, Paragraph 74. 


DIMENSIONS OF VOLUMES USED TO QUIET PULSATIONS 


Diameter, 

Inches 

Length, 

Inches 

Capacity, 

Cu. Ft. 

Diameter, 

Inches 

Length, 

Inches 

Capacity, 

Cu. Ft. 

8 

56 

1.65 

24 

30 

7.86 

9 

9 

0.33 

24 

60 

15.73 

9 

18 

0.67 

36 

6 

3.54 

9 

27 

1.00 

36 

18 

10.62 

9 

36 

1.33 

36 

24 

14.14 

9 

45 

1.67 

36 

42 

24.75 

9 

54 

2.00 

48 

3 

3.00 

18 

30 

4.43 

48 

7 

7.00 

24 

12 

3.14 

48 

16 

17.00 

24 

6 

1.57 

48 

25 

27.00 

24 

24 

6.28 

48 

34 

36.00 


Page 43, Paragraph 75. Where the combined errors of the venturi and 
orifice meters are plotted, the general effect is seen to be the same regardless of 
the kind of meter used. While for the smaller capacities there is a marked 
advantage shown by the volumes of larger diameter over those of smaller 
diameter (for equal capacities) yet the curves indicate that about 20 cu. ft. 
capacity is sufficient to bring the error due to pulsation below 2%, for all 
diameters. See also Tables 22, 23. 

Page 43, Paragraph 76. An attempt was made to establish a relation 
between the capacity of the minimum size of volume and the piston displace¬ 
ment of the compressor. Such a relationship might be useful if there were any 
close relation between the velocity pulsation and the pressure pulsation; but 
we have not been able to find any reason for assuming that any relation exists 
between piston displacement and volume capacity. 

Page 43, Paragraph 77. See curves in Fig. 38. 

Page 44, Paragraph 78. 

Data and Results for Pulsation Reduced by Orifices Combined with Volumes: 

Meter Used Data and Results Curves 

Venturi Table 24 Fig. 39, 40. 

33% & 70% Orifices Table 25 Fig. 41. 

















74 


EFFECT OF PULSATIONS ON FLOW OF GASES 


The curves in Fig. 39 show for the venturi meter the variation of error 
with drop in pressure for an orifice placed at the entrance to volumes of con¬ 
stant capacity ranging from 1/3 cu. ft. to 200 cu. ft. Points are also plotted 
for orifices at both entrance and exit to the volumes. It will be noted that 
two orifices, for the same constant volumes, gave a slightly greater reduction in 
the error. It was also observed while running that a volume fitted with two 
orifices instead of one, quite noticeably reduced the vibration and the sound 
effect which accompanies pulsating flow. 

The curves in Fig. 40 show for the venturi meter the effect of throttling by 
means of two orifices combined with different volumes for the complete range of 
volumes of constant capacity. The curves when read horizontally give the 
combinations of volume and drop in pressure for any given per cent of error. 
Likewise readings taken vertically give for a certain definite drop in pressure, 
the per cent error to be expected for any given volume. For example: For 5 % 
error and a drop in pressure of 2 inches of mercury, a volume of 3.54 cu. ft. 
would be required; and for a drop of 3 inches and volume of 2 cu. ft. the error 
would be 6 per cent. The curves in Fig. 41 show in a similar way the possible 
combinations for the 70% orifice meter when using the set of 24-inch volumes. 

Page 44, Paragraph 79. Some preliminary experiments were made with 
several mufflers (See Fig. 8). First a Powell auto muffler was used and directly 
following that a muffler was hastily constructed using tin funnels for the baffling 
units. This gave unusually good results, reducing the error to almost zero 
with a drop of a few inches of water. It was thought at the time that the prob¬ 
lem of pulsating flow was solved. However, when a new muffler was made of 
funnel sections more carefully constructed and a trial was made the previous 
results could not be duplicated. It required a drop in pressure of 6 inches of 
mercury with the new funnel muffler to reduce the error to 3.5 %. 

A fourth muffler (Type E, Fig. 8) larger in initial volume and containing four 
baffles with small holes was tried. This muffler as a simple volume tank gave 
an error of 4.3%, (which checked previous tests for the same conditions); and 
with the baffles in place gave an error of 2.5 % for a pressure drop of 3 or 4 
inches of water. 

Page 44, Paragraph 80. We were again convinced that the error of pulsa¬ 
tion can be reduced only by a loss in energy. Since the pulsating flow is an 
energetic fluctuation of velocity and pressure; in a large tank, or volume, these 
fluctuations become mutually eliminated, or dissipated. When throttling is used 
to quiet pulsations it is effective in so far as it absorbs the energy of the pulsations. 
The 33 % orifice meter gives less error than a larger orifice meter or the venturi 
meter because there is a greater unrestored pressure loss through it. When the 
excess energy of the pulsating flow is absorbed, the pulsations are eliminated. 
See also Table 26. 

Page 45, Paragraph 82. Velocity diagrams could be treated in a manner 
similar to an indicator card and integrated to determine the average pipe 
velocity. It would require the conversion of the velocity head diagram into a 
new diagram involving the square root of the velocity head before integrating, 
or the employment of a special form of rectifying planimeter. Such a method 
has been tried with partial success by Mr. H. N. Packard in his study of pul¬ 
sating flow. 

Use of correction factor: If the meter could be calibrated for pulsationless 


APPENDIX B 


75 


flow and the flow conditions under which it was to be used were to remain 
constant, then such a correction might be applied. The difficulties arising are 
as follows: 

1. It would be difficult to produce pulsationless flow in most commercial 
installations where pulsating flow is the source of the difficulty. 

2. It is doubtful whether or not true pulsationless flow could be assured. 

3. It would be difficult to establish the same quantity of flow for both 
pulsating and pulsationless flow. The exception might be in the case of a steam 
engine, where the steam used might be condensed and weighed as a check. 

4. Any number of slight variations are apt to arise in the flow conditions 
which would affect the amount of the error. A correction factor would have 
to be re-determined frequently. 

Use of a pulsating factor has been suggested by H. P. Westcott (*9) as 
applied to an orifice meter. A second line with a closed end is connected with 
the main line, parallel to it, ahead of the main orifice meter. It is subjected to 
the same static pressure and to the effect of pulsating flow under “no flow” 
conditions. The main meter reading will be influenced by two factors, the 
pulsating effect and the velocity of flow; the meter in the “dead-end” line is 
assumed to be influenced by the pulsating effect alone. The meter reading for 
pulsationless flow should also be found. A formula is proposed to express the 
relation between these three quantities: 

p 2 = (VF, * VDY 

Pi = corrected manometer reading for pulsating flow 
Pi = corrected manometer reading for pulsationless flow 
D = corrected manometer reading for “dead-end” flow 

If this relation holds true, then: 

_?W -1 
(Vp x * Vd ) 2 

Page 46, Paragraph 85. From Tables 27, 28, 29, 30 it can be seen that 
a meter when out of service in a “dead-end” line but otherwise subjected to the 
effect of pulsations may register a false flow reading ranging from 19 % to 239 % 
according to the type of meter. (See, also, Table 33.) 

Page 47, Paragraph 87. Table 31 contains the values for this ratio as com¬ 
puted from the data for the four points of line closure. 




76 


EFFECT OF PULSATIONS ON FLOW OF GASES 


APPENDIX C, TABLES. 

TABLE 11 EFFECT OF THROTTLING MANOMETER CONNECTIONS FOR VENTURI 

. METER (SEE P. 34, PAR. 57) 



Run, 

No. 

Throttling Plugs 

Kind 

Manometer Reading, 

Inches of Water 



Error 

Date 

Diam. 

Orifice, 

Inches 

Sizes, 

Inches 

of 

Flow 

At Orifice 
Head 

At Venturi 
Meter 

Corrected 
to 0.9 

Ratio 

VRatio 

Per 

Cent 



1 

2 

3 

4 

5 

6 

7 

8 

9 


28-Inch Vertical Water Manometer, Fig. 5 


1 

2 

0.1800 

diam. 

puls’less 

pulsating 

0.900 

.902 

9.68 

31.10 

9.68 

31.05 

3.21 

1.790 

79.0 

3 

0.0700 

f" length 

pulsating 

.905 

31.17 

31.00 

3.20 

1.788 

78.8 

4 

0.0635 


pulsating 

.900 

31.33 

31.33 

3.24 

1.800 

80.0 

5 

0.0465 


pulsating 

.899 

31.33 

31.34 

3.25 

1.803 

80.3 

6 

0.0420 


pulsating 

.904 

30.33 

30.20 

3.12 

1.766 

76.6 

7 

0.0200 


pulsating 

.920 

25.10 

24.65 

2.53 

1.593 

59.3 


Foxboro Differential Mercury Gage, Fig. 5 


7-27-21 


8 



puls’less 

pulsating 

0.900 

9 

0.1800 

diam. 

.893 

10 

0.0700 

P length 

pulsating 

.900 

11 

0.0635 


pulsating 

.902 

12 

0.0465 


pulsating 

.906 

13 

0.0420 


pulsating 

.902 

14 

0.0200 


pulsating 

.902 


9 

66 

9 

66 






20 

90 

21 

08 

2.18 

1 

479 

47 

0 

20 

50 

20 

50 

2.12 

1 

456 

45 

6 

20 

00 

19 

95 

2.07 

1 

437 

43 

7 

19 

50 

19 

39 

2.01 

1 

415 

41 

5 

17 

90 

17 

87 

1.85 

1 

360 

36 

0 

18 

60 

18 

58 

1.94 

1 

394 

39 

4 


TABLE 12 PER CENT ERROR FOR ORIFICE METERS, EFFECT DUE TO POINT 
OF MANOMETER CONNECTION (SEE P. 37. PAR. 62) 




Manometer 

Connection 

Kind 

Manometer Reading, 
Inches of Water 



Maxi- 

Error 

Compared 

Date 

Run, 

No. 

Above 

Orifice, 

Diams. 

Below 

Orifice, 

Diams. 

of 

Flow 

At 

Orifice 

Head 

At 

Orifice 

Meter 

Corrected 
to 0.9 

Ratio 

V Ratio 

mum 

Error, 

Per 

Cent 

with 

Standard 
Connection 
Per Cent 



1 

2 

3 

4 

5 

6 

7 

8 

9 

10 
































































































APPENDIX C 


/ ( 


33% Orifice Meter 


1 

2 

25 

2 

2o 

puls’less 

0.930 

22.88 

22.15 





2 

_2_ 

2 5 

2 

5a 

pulsating 

.931 

27.30 

26.40 

1.191 

1.092 

9.2 

93.9 

3 

1 

1 

2 

puls’less 

.935 

23.13 

22.25 





4 

1 

5 

pulsating 

.929 

27.60 

26.76 

1.203 

1.098 

9.8 

100.0 

5 

1 

2 

puls’less 

.934 

21 .40 

20.63 





6 

1 

2 

pulsating 

.935 

27.03 

26.05 

1.261 

1.123 

12.3 

125.5 

7 

1 

4 

puls’less 

.924 

20.08 

19.58 





8 

1 

4 

pulsating 

.929 

24.47 

24.73 

1.262 

1.123 

12.3 

125.5 

9 

1 

8 

puls’less 

.932 

20.28 

19.60 





10 

1 

8 

pulsating 

.930 

24.53 

23.75 

1.210 

1.100 

10.0 

102.0 

11 

1 

19 

puls’less 

.935 

20.43 

19.70 





12 

1 

19 

pulsating 

.931 

24.13 

23.33 

1.185 

1.090 

9.0 

91.8 


40% Orifice Meter 


1-3-22 

13 

_2_ 

_ 2 _ 

puls’less 

0.937 

10.90 

10.47 






14 


2 

2 5 

pulsating 

.944 

16.77 

16.03 

1.531 

1.237 

23.7 

100.0 


15 

i 

1 

puls’less 

.948 

11.03 

10.48 






16 

i 

1 

2 

pulsating 

.943 

16.97 

16.01 

1.530 

1.237 

23.7 

100.0 


50% Orifice Meter 


1-3-22 

17 

T5 

2 

2 5 

puls’less 

0.936 

4.35 

4.18 





18 

15 

2 

2 5 

pulsating 

.936 

10.27 

6.89 

2.362 

1.536 

53.6 


19 

l 

1 

2 

puls’less 

.940 

4.28 

4.11 





20 

l 

1 

2 

pulsating 

.934 

10.87 

10.47 

2.552 

1.599 

59.9 


60 %• Orifice Meter 


1-3-22 

21 

2 

2 5 

2 

2 5 

puls’less 

0.937 

1.92 

1.846 





22 

. 2 

2 5 

2 

pulsating 

.937 

6.90 

6.630 

3.590 

1.898 

89.8 


23 

1 

1 

2 

puls’less 

.944 

1.90 

1.810 





24 

1 

1 

2 

pulsating 

.935 

7.03 

6.640 

3.670 

1.915 

91.5 


70% Orifice Meter 


25 

2 

2 

pill.s’lpss 

0 977 

1 010 

0 930 




\ 

26 

2 5 

2 

2 5 

2 5 

2 

2 5 

pulsating 

.987 

5.306 

4.840 

5.210 

2.283 

128.3 

97.6 

27 

1 

1 


982 

1 010 

0 926 





28 

1 

1 

2 

pulsating 

.982 

5.400 

4.950 

5.340 

2.315 

131.5 

100.0 

99 

1 

2 


985 

0 643 

0.588 





30 

1 

2 

pulsating 

.985 

4.113 

3.755 

6.380 

2.525 

152.5 

117.0 

31 

1 

4 


976 

0 510 

0 471 





32 

1 

4 

pulsating 

.988 

3.430 

3.120 

6.630 

2.575 

157.5 

120.0 

33 

1 

8 

puls’less 

.975 

0.510 

0.471 





34 

1 

8 

pulsating 

.983 

3.320 

3.040 

6.460 

2.540 

154.0 

117.2 

35 

1 

19 

puls’less 

.975 

0.543 

0.502 





36 

1 

19 

pulsating 

.983 

3.220 

2.940 

5.870 

2.420 

142.0 

108.0 


80% Orifice Meter 


1-3-22 

37 

2 

2 5 

2 

2 5 

puls’less 

0.980 

0.460 

0.422 






38 

2 

15 

2 

25 

pulsating 

.970 

3.300 

3.065 

7.260 

2.695 

169.5 

93.0 


39 

1 

1 

2 

puls’less 

.980 

0.432 

0.397 






40 

1 

1 

2 

pulsating 

.969 

3.400 

3.160 

7.960 

2.820 

182.0 

100.0 





























































































































78 


EFFECT OF PULSATIONS ON FLOW OF GASES 


TABLE 12 — Continued 


Date 

Run, 

No. 

Manometer 

Connection 

Kind 

of 

Flow 

Manometer Reading, 
Inches of V’ater 

Ratio 


Maxi¬ 

mum 

Error, 

Per 

Cent 

Error 

Compared 

with 

Standard 
Connection 
Per Cent 

Above 

Orifice, 

Diams. 

Below 

Orifice, 

Diams. 

At 

Orifice 

Head 

At 

Orifice 

Meter 

Corrected 
to 0.9 

v'Ratio 



1 

2 

3 

4 

5 

6 

7 

8 

9 

10 


90% Orifice Meter 


1-3-22 

41 

2 

SJ 

2 

2 5 

puls’less 

0.970 

0.175 

0.161 





42 

2 

25 

2 

2A 

pulsating 

.989 

2.080 

1.892 

11.750 

3.430 

243.0 


43 

1 

1 

2 

puls’less 

.969 

0.090 

0.084 





44 

1 

1 

2 

pulsating 

.985 

1.880 

1.720 

20.450 

4.520 

352.0 


95% Orifice Meter 


1-3-22 

45 

T5 

2 

2 5 

puls’less 

0.945 

0.055 

0.0524 


46 

27 

2 

2 5 

pulsating 

.990 

1.520 

1.3820 


47 

1 

1 

2 

puls’less 

.950 

0.010 

0.0095 


48 

1 

1 

2 

pulsating 

.990 

1.060 

0.9640 


26.40 5.140 


101.80 10.080 


414.0 

908.0 


45 .6 


100.0 


100% Orifice Meter 


1-3-22 

49 

A 

2 

puls’less 

0.900 

0.007 

0.0070 






50 

^ D 

2 

J5 

2 

2 5 

pulsating 

.930 

1.032 

1.0000 

143.0 

11.96 

10.96 



51 

1 

x 

puls’less 

.940 

0.007 

0.0067 






52 

1 

1 

2 

pulsating 

.940 

0.992 

0.9950 

141.5 

11.90 

10.90 

100.0 


53 

1 

2 

puls’less 

.922 

0.007 

0 0068 






54 

1 

2 

pulsating 

.922 

1.292 

1.2620 

186.0 

13.65 

12.65 



55 

1 

4 

puls’less 

.931 

0.007 

0.0068 






56 

1 

4 

pulsating 

.931 

1.232 

1.1900 

175.0 

13.23 

12.23 



57 

1 

8 

puls’less 

.932 

0.017 

0.0160 






58 

1 

8 

pulsating 

.937 

0.952 

0.9150 

57.2 

7.56 

6.56 



59 

1 

19 

puls’less 

.929 

0.038 

0.0370 






60 

1 

19 

pulsating 

.935 

0.802 

0.7720 

20.8 

4.67 

3.67 



TABLE 13 ERROR COMPARED WITH THAT FOR STANDARD CONNECTIONS 
(1-DIAMETER ABOVE, DIAMETER BELOW 7 ORIFICE; (SEE P. 37, PAR. 62) 


No. 

Size of 
Orifice, 

Per Cent 

Point 

of Attachment, (A Above, B Below Orifice) Pipe Diams. 

J5 A, /jB 

1 A, 5 B 

1 A, 2 B 

1 A, 4 B 

1 A, 8 B 

1 A, 19 B 





E 

rror, Per Cen 

t 


1 

33 

93.0 

100 

125.5 

125.5 

102.0 

91.8 

2 

40 

100.0 

100 





3 

50 

91.0 

100 





4 

60 

98.2 

100 





5 

70 

97.6 

100 

117.0 

120.0 

117.2 

108.0 

6 

80 

93.0 

100 





7 

90 

69.0 

100 





8 

95 

45.6 

100 





9 

100 

100.6 

100 

116.0 

112.0 

60.0 

34.0 

Average 








(omitting 7, 8 , 9) 

96.3 

100 

121.2 

122 . 8 . 

109.6 
















































































































































APPENDIX C 79 


TABLE 14 EFFECT OF VOLUMES INSERTED IN MANOMETER CONNECTIONS 

(SEE P. 37, PAR. 61) 


Date 

Run, 

No. 

Pipettes, H" Diam., 

9" Long 

Kind 

of 

Flow 

Manometer Reading, 
Inches of Water 

Ratio 


Error 

Per 

Cent 

Total 

Number 

Used 

Position at 
Orificer Meter 

At Orifice 
Head 

At Orifice 
Meter 

Corrected 
to 0.9 

v' Ratio 



1 

2 3 

4 

5 

6 

7 

8 

9 

10 


40% Orifice Meier Using 2S-Inch Vertical Manometer With Glass Pipettes 


1-20-22 

1 

0 



puls’less 

puls’less 

0 918 

10.53 

10.53 

10.33 

10.33 





2 

2 

1 above 

1 below 

.918 

1.000 

1.000 

0.0 


3 

0 



pulsating 

pulsating 

918 

17.07 

15.17 

16.72 

14.81 

1.620 

1.433 

1.273 
1.197 

27.3 

19.7 


4 

2 

1 above 

1 below 

.921 


5 

1 

none 

1 below 

pulsating 

.916 

16.93 

16.65 

1.602 

1.267 

26.7 


6 

1 

1 above 

none 

pulsating 

.915 

15.40 

15.15 

1.466 

1.210 

21.0 


7 

2 

2 above 

none 

pulsating 

.913 

13.27 

13.09 

1.266 

1.125 

12.5 

70% 

Orifice 

Meter, 

Using 

6-Inch Inclined Manometer 

With Glass Pipettes 


1-20-22 

8 

0 



puls’less 

puls’less 

.914 

0 955 

0 940 




9 

2 

1 above 

1 below 

.916 

0.960 

0.943 

1.002 

1.001 

0.1 


10 

0 



pulsating 

pulsating 

.904 

5.127 

5.110 

5 430 

2.333 

133.3 


11 

2 

1 above 

1 below 

.908 

4.427 

4.380 

4.660 

2.160 

116.0 


12 

1 

none 

1 below 

pulsating 

.905 

4.800 

4.780 

5.090 

2.255 

125.5 


13 

1 

1 above 

none 

pulsating 

.906 

4.687 

4.660 

4.950 

2.225 

122.5 


14 

2 

2 above 

none 

pulsating 

.908 

4.180 

4.140 

4.410 

2.100 

110.0 


TABLE 15 EFFECT OF VOLUMES INSERTED IN MANOMETER CONNECTIONS 

(SEE P. 37, PAR. 61) 




Volume Units, 

1|" Diam., 1" Long 

Kind 

Manometer Reading, 
Inches of Water 



Error 

Date 

Run 

No. 

Total 

Number 

Used 

Position at 
Orifice Meter 

of 

Flow 

At 

Orifice 

Head 

At 

Orifice 

Meter 

Corrected 
to 0.9 

Ratio 

v Ratio 

Per 

Cent 



1 

2 

3 

4 

5 

6 

7 

8 

9 

10 


70% Orifice Meter, Using 6-inch Inclined Manometer with Volume Units 


1 

o 



puls’less 

0.901 

1.12 

1.12 




2 

o 



pulsating 

.902 

5.60 

5.58 

4.99 

2.235 

123.5 

3 

1—N 

1 above 

none 

pulsating 

.900 

5.40 

5.40 

4.83 

2.200 

120.0 

4 

2—N 

1 above 

1 below 

pulsating 

.902 

5.43 

5.41 

4.83 

2.200 

120.0 

5 

2—N 

2 above 

none 

pulsating 

.902 

5.27 

5.26 

4.70 

2.167 

116.7 

6 

4—N 

2 above 

2 below 

pulsating 

.900 

5.40 

5.40 

4.83 

2.200 

120.0 

7 

3—N 

3 above 

none 

pulsating 

.900 

5.10 

5.10 

4.56 

2 135 

113.5 

8 

6—N 

3 above 

3 below 

pulsating 

.901 

5.30 

5.30 

4.74 

2.179 

117.9 

9 

4—N 

4 above 

none 

pulsating 

.902 

5.00 

4.98 

4.46 

2.113 

111.3 

10 

8-N 

4 above 

4 below 

pulsating 

.901 

5.16 

5.15 

4.61 

2.145 

114.5 

11 

5-N 

5 above 

none 

pulsating 

.902 

4.83 

4.81 

4.30 

2.075 

107.5 

12 

10—N 

5 above 

5 below 

pulsating 

.902 

4.84 

4.82 

4.31 

2.076 

107.6 

13 

6—N 

6 above 

none 

pulsating 

.903 

4.86 

4.84 

4.33 

2.080 

108.0 

14 

12—N 

12 above 

none 

pulsating 

.903 

4.92 

4.90 

4.38 

2.093 

109.3 

1 ^ 

6—N 











12-0 

6 above 

12 below 

pulsating 

.902 

4.49 

4.48 

4.02 

2.005 

100.5 

16 

6-0 

6 above 

none 

pulsating 

.903 

4.71 

4.69 

4.20 

2.047 

104.7 

17 

12-0 

6 above 

6 below 

pulsating 

.901 

4.70 

4.70 

4.20 

2.047 

104.7 

18 

12-0 

12 above 

none 

pulsating 

.902 

4.61 

4.59 

4.11 

2.025 

102.5 
























































































































80 


EFFECT OF PULSATIONS ON FLOW OF GASES 


TABLE 16 MAXIMUM PER CENT ERROR FOR ORIFICE METER 


(SEE P. 39, PAR. 66) 


Date 

Run 

No. 

Orifice Used 

Kind 

of 

Flow 

Manometer Reading, 
Inches of Water 

Ratio 


Error 

Per 

Cent 

Size, 

Per 

Cent 

Diam., 

Inches 

At 

Orifice 

Head 

At 

Orifice 

Meter 

Corrected 
to 0.9 

"^Ratio 



1 

2 

3 

4 

5 

6 

7 

8 

9 

8-13-21 

1 

33 

1.098 

pnls’less 

0 902 

22 070 

22.000 





2 

33 

1.098 

pulsating 

.905 

26.470 

26.350 

1.196 

1.092 

9.2 


3 

50 

1.530 

pnls’less- 

914 

3 930 

3.780 





4 

50 

1.530 

pulsating 

.900 

10.000 

10.000 

2.642 

1.623 

62.3 


5 

60 

1.836 

pnls’less 

914 

1 685 

1.660 





6 

60 

1.836 

pulsating 

.894 

6.420 

6.460 

3.950 

1.986 

98.5 


7 

70 

2.142 

pnls’less 

914 

0 800 

0.788 





8 

70 

2.142 

pulsating 

.910 

3.800 

3.760 

4.770 

2.185 

118.5 


9 

80 

2.448 

puls’less 

.898 

0.348 

0.349 





10 

80 

2.448 

pulsating 

.904 

2.720 

2.713 

7.780 

2.790 

179.0 


11 

90 

2.754 

puls’less 

.918 

0.079 

0.077 





12 

90 

2.754 

pulsating 

.878 

0.807 

0.828 

10.240 

3.200 

220.0 

1-3-22 

13 

33 

1.098 

puls’less 

.935 

23.130 

22.250 





14 

33 

1.098 

pulsating 

.929 

27.600 

26.750 

1.203 

1.098 

9.8 


15 

40 

1.224 

puls’less 

.948 

11.030 

10.490 





16 

40 

1.224 

pulsating 

.943 

16.970 

16.000 

1.525 

1.235 

23.5 


17 

50 

1.530 

puls’less 

.940 

4.280 

4.100 





18 

50 

1.530 

pulsating 

.934 

10.970 

10.480 

2.560 

1.600 

60.0 


19 

60 

1.836 

puls’less 

.944 

1.900 

1.810 





20 

60 

1.836 

pulsating 

.935 

7.030 

6.640 

3.670 

1.915 

9.15 


21 

70 

2.142 

puls’less 

.982 

1.010 

0.927 





22 

70 

2.142 

pulsating 

.982 

5.400 

4.950 

5.340 

2.315 

131 5 


23 

80 

2.488 

puls’less 

.980 

0.432 

0.397 





24 

80 

2.488 

pulsating 

.969 

3.400 

3.160 

7.960 

2.820 

182.0 

• 

25 

90 

2.754 

puls’less 

.969 

0.090 

0.084 





26 

90 

2.754 

pulsating 

.985 

1.880 

1.720 

20.450 

4.520 

352.0 


27 

95 

2.907 

puls’less 

.950 

0.010 

0.0095 





28 

95 

2.907 

pulsating 

.990 

1.060 

C.964 

101.800 

10.080 

908.0 


29 

100 

3.060 

puls’less 

.940 

0.007 

0.0067 





30 

100 

3.060 

pulsating 

.940 

0.992 

0.950 

142.000 

11.900 

1090.0 

1-19-22 

31 

40 

1.224 

puls’less 

.932 

10.830 

10.470 





32 

40 

1.224 

pulsating 

.905 

17.030 

16.950 

1.620 

1.272 

27.2 


33 

50 

1.530 

puls’less 

.907 

4.100 

4.070 





34 

50 

1 .530 

pulsating 

.920 

10.800 

10.600 

2.610 

1.615 

61.5 


35 

60 

1.836 

puls’less 

.917 

1.850 

1.816 





36 

60 

1.836 

pulsating 

.920 

7.030 

6.780 

3.730 

1.932 

93.2 


37 

70 

2.142 

puls’less 

.909 

0.670 

0.664 





38 

70 

2.142 

pulsating 

.919 

3.880 

3.800 

5.730 

2.395 

139.5 


39 

80 

2.488 

puls’less 

.903 

0.410 

0.408 





40 

80 

2.488 

pulsating 

.905 

0.287 

0.286 

7.000 

2.647 

164.7 


41 

90 

2.754 

puls’less 

.914 

0.080 

0.079 





42 

90 

2.754 

pulsating 

.924 

1.170 

1.140 

14.800 

3.845 

284.5 


43 

50 

1.530 

puls’less 

.901 

4.000 

3.990 




6-28-22 

44 

50 

1.530 

pulsating 

.905 

8.270 

8.220 

2.060 

1.435 

43.5 


45 

70 

2.142 

puls’less 

.906 

4.975 

4.950 





46 

70 

2.142 

pulsating 

.912 

25.800 

25.750 

5.200 

2.380 

138.0 


47 

80 

2.488 

puls’less 

.902 

2.195 

2.190 





48 

80 

2.488 

pulsating 

.900 

15.540 

15.540 

7.190 

2.655 

165.5 


49 

90 

2.754 

puls’less 

.903 

0.460 

0.458 





50 

90 

2.754 

pulsating 

.910 

5.800 

5.740 

12.530 

3.543 

254.3 


51 

40 

1.224 

puls’less 

.918 

10.530 

10.330 




1 -20-22 

52 

40 

1.224 

pulsating 

.918 

17.070 

16.720 

1.620 

1.273 

27.3 


53 

70 

2.142 

puls’less 

.914 

0.955 

0.940 





54 

70 

2.142 

pulsating 

.904 

5.127 

5.110 

5.430 

2.333 

133.3 


55 

70 

2.142 

puls’less 

.901 

1.120 

1.118 





56 

70 

2.142 

pulsating 

.902 

5.600 

5.580 

4.990 

2.235 

123.5 







































































































































APPENDIX C 


81 


TABLE 17 PER CENT ERROR FOR VENTURI METER, PULSATIONS 
QUIETED BY THROTTLING (SEE P. 42, PAR. 73) 


Date 

Run 

No. 

Drop 
Through 
Valve, In. 
Mercury 

Manometer Readings, 

Inches of Water 

Ratio 


Error 

Per 

Cent 

v" Ratio 

At Orifice 
Head 

At Venturi 
Meter 

Corrected 
to 0.9 



1 

2 

3 

4 

5 

6 

7 

2-15-21 

1 

puls’less 

0.901 

9.55 

9.54 





2 

0.03 

.900 

11.37 

11.37 

1.193 

1.093 

9.3 


3 

0.93 

.900 

11.24 

11.24 

1.182 

1.087 

8.7 


4 

1.93 

.899 

10.75 

10.74 

1.129 

1.063 

6.3 


5 

4.59 

.900 

10.14 

10.14 

1.064 

1.032 

3.2 


6 

6.54 

.899 

9.99 

9.98 

1.047 

1.023 

2.3 


7 

7.01 

.902 

9.86 

9.84 

1.031 

1.015 

1.5 


8 

8.16 

.903 

9.71 

9.68 

1.013 

1.007 

0.7 


9 

9.82 

.901 

9.74 

9.73 

1.021 

1.011 

1.1 


10 

12.06 

.908 

9.79 

9.70 

1.017 

1.009 

0.9 


11 

puls’less 

900 

9.58 

9.58 



.... 


12 

0.06 

.899 

11.69 

11.72 

1.222 

1.105 

10.5 


13 

0.45 

.903 

11.57 

11.53 

1.204 

1.097 

9.7 


14 

1.93 

.902 

10.79 

10.76 

1.120 

1.058 

5.8 


15 

4.18 

.912 

10.33 

10.20 

1.063 

1.031 

3.1 


16 

5.90 

.895 

9.97 

10.05 

1.050 

1.025 

2.5 


17 

5.82 

.893 

9.91 

10.09 

1.052 

1.026 

2.6 


18 

7.36 

.898 

9.88 

9.90 

1.033 

1.016 

1.6 


19 

9.64 

.901 

9.81 

9.80 

1.022 

1.011 

1.1 


20 

12.42 

.914 

9.89 

9.72 

1.015 

1.008 

0.8 

2-28-21 

21 


910 

9 85 

9.74 




22 

0.24 

.922 

12.33 

12.05 

1.238 

1.113 

11.3 


23 

0.48 

.919 

12.08 

11.82 

1.215 

1.102 

10.2 


24 

0.48 

.919 

12.12 

11.86 

1.218 

1.104 

10.4 


25 

0.75 

.902 

11.69 

11.67 

1.198 

1.095 

9.5 


26 

2.60 

.915 

10.97 

10.79 

1.108 

1.053 

5.3 


27 

3.86 

.933 

10.87 

10.48 

1.076 

1.037 

3.7 


28 

6.40 

.930 

10.33 

10.01 

1.028 

1.014 

1.4 


29 

8.35 

.928 

10.23 

9.91 

1.018 

1.009 

0.9 


30 

12.85 

.944 

10.23 

9.77 

1.004 

1.002 

0.2 


31 

puls’less 

.931 

9.63 

9.32 





32 

0.00 

.907 

11.91 

11.83 

1.272 

1.129 

12.9 

4-22-21 

33 

1.00 

.924 

11.51 

11.20 

1.202 

1.096 

9.6 


34 

3.20 

.964 

10.95 

10.23 

1.100 

1.048 

4.8 


35 

4.90 

.965 

10.59 

9.86 

1.058 

1.028 

2.8 


36 

8.90 

.902 

9.59 

9.57 

1.028 

1.014 

1.4 


37 

18.40 

.955 

10.02 

9.42 

1.010 

1.005 

0.5 


38 

puls’less 

.898 

9.40 

9.42 



.... 

5-6-21 

39 

0.20 

.891 

30.90 

31.20 

3.320 

1.820 

82.0 


40 

2.00 

.939 

15.52 

14.89 

1.580 

1.258 

25.8 


41 

4.50 

.912 

11.20 

11.00 

1.170 

1.082 

8.2 


42 

7.90 

.935 

10.50 

10.10 

1.072 

1.035 

3.6 


43 

12.00 

.941 

10.40 

9.95 

1.057 

1.027 

2.7 


44 

18.50 

.895 

9.70 

9.76 

1.036 

1.018 

1.8 


45 

0.00 

.937 

11.75 

11.30 

1.200 

1.095 

9.5 


46 

0.20 

.945 

11.43 

10.90 

1.159 

1.077 

7.7 


47 

1.10 

.945 

10.47 

9.95 

1.057 

1.027 

2.7 


48 

2.80 

.931 

9.85 

9.53 

1.012 

1.007 

-0.7 


49 

4.60 

.934 

9.85 

9.50 

1.009 

1.005 

-0.5 


50 

6.80 

.911 

9.51 

9.40 

0.997 

0.999 

-o.i 


51 

. 12.00 

.937 

9.76 

9.37 

0.996 

0.998 

-0.2 


52 

puls’less 

.900 

9.25 

9.25 



• . . . 


53 

0.00 

.900 

31.50 

31.50 

3.410 

1.845 

84.5 


54 

0.00 

.911 

32.80 

32.60 

3.350 

1.830 

83.0 


55 

0.00 

.905 

28.82 

28.70 

3.120 

1.768 

76.8 
















































82 


EFFECT OF PULSATIONS ON FLOW OF GASES 


TABLE IS PER CENT ERROR FOR ORIFICE METER, PULSATIONS 
QUIETED BY THROTTLING (SEE P. 42, PAR: 73) 


Date 

Run 

No. 

Orifice Used 

Drop 

Thru 

Valve, 

Inches, 

Mercury 

Manometer Readings, 
Inches of Water 

Ratio 

V 


Error 

Per 

Cent 

Size 

Per 

Cent 

Diam., 

Inches 

At Orifice 
Head 

At Orifice 
Meter 

Corrected 
to 0.9 

Ratio 



1 

2 

3 

4 

5 

6 

7 

8 

9 

5-4-21 

1 

33 

1.098 

puls’less 

0.900 

23.17 

23.17 






2 

. . . 

. 

0.50 

.870 

25.90 

26.80 

1.156 

1 

.075 

7.5 


3 

. . . 


2.40 

.938 

25.13 

24.10 

1.03; 

1 

.018 

1.8 


4 

• . • 


5.10 

.900 

23.90 

23.90 

1.03C 

1 

.015 

1.5 


5 

. . . 


5.90 

.918 

24.43 

24.00 

1.03c 

1 

.016 

1.6 


6 

. • . 


6.40 

.905 

23.77 

23.61 

1.02C 

1 

.010 

1.0 


7 

. . . 


11.20 

.905 

23.77 

23.61 

1.02C 

1 

.010 

1.0 


8 



17.00 

.888 

23.83 

24.15 

1.040 

1 

.020 

2.0 


9 



puls’less 

.935 

23.13 

22.25 



.... 



10 

. . • 


0.0 

.929 

27.60 

26.75 

1.200 

1 

.095 

9.5 

1-13-22 

11 

• . . 


puls’less 

.927 

23.20 

22.50 






12 

. . . 


0.25 

.922 

27.60 

26.95 

1.198 

1 

.093 

9.3 


13 

. . . 


0.95 

.928 

25.10 

24.30 

1.080 

1 

.040 

4.0 


14 

. . . 


1.85 

.921 

23.50 

22.95 

1.020 

1 

.010 

1.0 


15 



3.10 

.931 

23.20 

22.50 

1.000 

1 

.000 

0.0 


16 



4.45 

.933 

23.50 

22.65 

1.008 

1 

.004 

0.4 


17 

. . . 


5.90 

.935 

23.60 

22.75 

1.012 

1 

.006 

0.6 


18 

• . . 


8.40 

.938 

23.70 

22.75 

1.012 

1 

.006 

0.6 


19 

. . . 

. 

12.30 

.931 

23.40 

22.63 

1.008 

1 

.004 

0.4 


20 

. . . 


18.00 

.938 

23.70 

22.75 

1.010 

1 

.005 

0.5 


21 



puls’less 

.902 

22.07 

22.00 





6-28-22 

22 



0.0 

.905 

26.47 

26.35 

1.196 

1 

.092 

9.2 


23 



0.65 

.915 

25.40 

25.00 

1.138 

1 

.066 

6.6 


24 



1.05 

.906 

23.93 

23.76 

1.079 

1 

038 

3.8 


25 

... 


2.40 

.912 

23.30 

23.00 

1.057 

1 

026 

2.6 


26 



4.40 

.910 

22.83 

22.60 

1.027 

1 

013 

1.3 

6-28-22 

27 

50 

1.530 

puls’less 

.902 

4.000 

3.990 






28 



0.0 

.905 

8.270 

8.220 

2.060 

1 

435 

43.5 


29 



0.65 

.909 

8.367 

8.280 

2.075 

1 

440 

44.0 


30 



1.00 

.906 

6.803 

6.760 

1.693 

1 

300 

30.0 


31 



2.20 

.908 

5.263 

5.220 

1.308 

1 

143 

14.3 


32 



4.30 

.901 

4.500 

4.500 

1.128 

1 

062 

6.2 


33 



6.40 

.903 

4.327 

4.315 

1.080 

1 

040 

4.0 


34 

... 


8.40 

.900 

4.237 

4.237 

1.062 

1 

030 

3.0 


35 

70 


puls’less 

.982 

1.01 

0.926 





12-23-21 

36 

. . . 


0.00 

.982 

5.40 

4.950 

5.350 

2. 

275 

127.5 


37 



puls’less 

.938 

0.67 

0.635 





1-13-22 

38 



0.25 

.944 

4.04 

3.855 

6.071 

2. 

460 

146.0 


39 


. 

1.00 

.934 

2.63 

2.535 

4.000 

2. 

000 

100.0 


40 

*•' * 


2.00 

.934 

1.62 

1.560 

2.460 

1. 

570 

57.0 


41 



4.20 

.939 

0.89 

0.854 

1.394 

1. 

160 

16.0 


42 



8.30 

.946 

0.73 

0.695 

1.094 

1 . 

045 

4.5 


43 



12.30 

.945 

0.73 

0.695 

1.094 

1 . 

045 

4.5 


44 



16.90 

.938 

0.72 

0.692 

1.090 

1 . 

043 

4.3 

6-28-22 

45 



19.20 

.944 

0.72 

0.677 

1.067 

1 . 

033 

3.3 

46 



puls’less 

.910 

5.00 

4.95 




47 



0.10 

.912 

25.80 

25.75 

5.200 

2. 

380 

138.0 


48 



0.60 

.919 

21.57 

21.15 

4.270 

2. 

066 

106.6 


49 



1.30 

.915 

15.19 

14.93 

3.020 

1 . 

747 

74.7 


50 



2.20 

.900 

9.47 

9.47 

1.911 

1 . 

382 

38.2 


51 



4.30 

.901 

6.31 

6.30 

1.272 

1 . 

129 

12.9 






































































































APPENDIX C 


83 


TABLE 18 PER CENT ERROR FOR ORIFICE METER, PULSATIONS 
QUIETED BY THROTTLING (SEE P. 42, PAR. 73 ) —Continued 


Date 

Run, 

No. 

Orifie 

Size 

Per 

Cent 

e L'sed 

Diam., 

Inches 

Drop 

Through 

Valve, 

Inches, 

Mercury 

Manometer Readings, 
Inches of Water 

Ratio 


Error 

Per 

Cent 

At Orifice 
Head 

At Orifice 
Meter 

Corrected 
to 0.9 

"'/Ratio 



1 

2 

3 

4 

5 

6 

7 

8 

9 


52 




6 . 

10 

0.906 

5 

72 

5.68 

1 

147 

1 

071 

7 

1 


53 




8 . 

40 

.930 

5 

59 

5.40 

1 

090 

1 

043 

4 

3 


54 




9. 

60 

.912 

5 

43 

5.36 

1 

082 

1 

041 

4 

1 

6-29-22 

55 

80 

2 

448 

puls 

’less 

.902 

2 

195 

2.190 








56 




0 

20 

.900 

15 

540 

15.540 

7 

010 

2 

655 

165 

5 


57 




0 

65 

.910 

12 

800 

12.650 

5 

750 

2 

395 

139 

5 


58 




1 

20 

.914 

10 

740 

10.590 

4 

810 

2 

195 

119 

5 


59 




2 

30 

.907 

4 

940 

4.900 

2 

230 

1 

490 

49 

0 


60 




4 

50 

.910 

2 

720 

2.690 

1 

220 

1 

104 

10 

4 


61 



. . . • 

6 

40 

.916 

2 

400 

2.360 

1 

072 

1 

034 

3 

4 


62 




8 

40 

.904 

2 

340 

2.330 

1 

060 

1 

030 

3 

0 


63 




11 

10 

.884 

2 

320 

2.345 

1 

068 

1 

.033 

3 

3 


64 

90 

2 

.754 

puls 

’less 

.903 

0 

460 

0.458 



. 





65 


# 


0 

17 

.910 

6 

800 

5.740 

12 

530 

3 

.543 

254 

3 


66 




0 

70 

.910 

5 

360 

5.310 

11 

600 

3 

.404 

240 

4 


67 




1 

35 

.905 

4 

610 

4.580 

10 

.000 

3 

.160 

216 

0 


68 




2 

65 

.907 

1 

250 

1.240 

2 

.710 

1 

.645 

64 

5 


69 




4 

30 

.902 

0 

470 

0.469 

1 

.025 

1 

.012 

1 

2 

- 

70 




6 

20 

-.902 

0 

430 

0.430 

0 

.938 

0 

.967 

-3 

.3 


71 




7 

40 

.916 

0 

420 

0.413 

0 

.902 

0 

.950 

-5 

.0 


72 




8 

60 

.895 

0 

.440 

0.443 

0 

.970 

0 

.985 

- 1 

.5 


73 




11 

.15 

.886 

0 

.550 

0.559 

1 

.220 

1 

.105 

10 

5 


Note: — Inclined manometer was used for Runs 46 to 73. To reduce Column 6 to inches 
of water, multiply by 0.17. 
































































84 


EFFECT OF PULSATIONS ON FLOW OF GASES 


TABLE 19 PER CENT ERROR FOR FLANGE NOZZLE-METER, PULSATIONS 
QUIETED BY THROTTLING (SEE P. 42, PAR. *73) 




Nozzle Used 

Date 

Run 


No. 

Diam., 

Length 




Inches 

Inches 



1 

2 

6-15-22 

1 

1 | 

nice 

CO 


2 




3 




4 

.... 



5 




6 




7 




8 




9 




10 




11 




12 




13 



6-16-22 

14 

H 

3f 


15 




16 




17 




18 




19 




20 




21 




22 




23 




24 




25 



6-26-22 

26 

2 

3f 


27 




28 




29 




30 




31 




32 




33 




34 




35 




36 



6-27-22 

37 

2 * 

3f 


38 




39 




40 




41 




42 




43 




44 




45 




Drop 

Through 

Manometer Readings, 
Inches of Water 

Ratio 

V / .Ratio 

Error 

Per 

Cent 

Valve, 

Inches, 

Mercury 

At Orifice 
Head 

At Nozzle 
Meter 

Corrected 
to 0.9 

3 

4 

5 

6 

7 

8 

9 

puls’less 

0.908 

3 

.23 

3 

.210 






, . 

0.0 

.907 

10 

.10 

10 

.020 

3 

.120 

1 

.765 

76 

.5 

1.3 

.922 

5 

.50 

5 

.370 

1 

.672 

1 

.293 

29 

.3 

2.4 

.900 

4 

.05 

4 

.050 

1 

.260 

1 

.122 

12 

.2 

3.9 

.900 

3 

.63 

3 

.630 

1 

.130 

1 

.063 

6 

.3 

6.3 

.900 

3 

.49 

3 

.490 

1 

.120 

1 

.060 

6 

.0 

8.7 

.905 

3 

.38 

3 

.365 

1 

.080 

1 

.040 

4 

.0 

10.0 

.900 

3 

.29 

3 

.290 

1 

.026 

1 

.013 

1 

.3 

11.4 

.895 

3 

.36 

3 

.380 

1 

.050 

1 

.025 

2 

.5 

puls’less 

.910 

5 

.72 

5 

.660 




• • . . 



0.0 

.902 

11 

.60 

11 

.570 

2 

.025 

1 

.422 

42 

.2 

puls’less 

.900 

5 

.57 

5 

.570 







0.0 

. .902 

11 

.77 

11 

.730 

2 

.100 

1 

.450 

45 

.0 

puls’less 

.899 

1 

.663 

1 

.664 



# 




0.00 

.903 

6 

.300 

6 

.280 

3 

.775 

1 

.943 

94 

.3 

0.65 

.913 

4 

.830 

4 

.760 

2 

860 

1 

.690 

69 

0 

1.10 

.907 

4 

.530 

4 

500 

2 

.700 

1 

.642 

64 

2 

1.15 

.911 

3 

.750 

3 

730 

2 

240 

1 

.497 

49 

7 

1.30 

.895 

4 

250 

4 

270 

2 

665 

1 

.632 

63 

2 

2.40 

.899 

2 

470 

2 

480 

1 

490 

1 

.218 

21 

8 

3.10 

.893 

2 

140 

2 

155 

1 

294 

1 

.138 

13 

8 

4.50 

.897 

1 

953 

1 

960 

1 

177 

1 

083 

8 

3 

6.20 

.914 

1 

900 

1 

870 

1 

122 

1 

061 

6 

1 

puls’less 

.900 

1 

636 

1 

636 







0.00 

.901 

6 

170 

6 

160 

3 

770 

1 

942 

94 

2 

puls’less 

.901 

2 

883 

2 

880 





• • • . 


0.0 

.910 

17 

270 

16 

880 

5 

860 

2 

420 

142 

0 

0.8 

.901 

14 

120 

14 

110 

4 

900 

2 

215 

121 . 

5 

1.5 

.895 

9 

907 

9 

960 

3 

460 

1 

860 

86 

0 

2.7 

.901 

5 

160 

5 

160 

1 

790 

1 

338 

33. 

8 

3.4 

.905 

4 

160 

4 

140 

1 

436 

1 

197 

19. 

7 

4.7 

.916 

3. 

593 

. 3 

535 

1 

228 

1 

109 

10 . 

9 

puls’less 

.917 

2 . 

757 

2 . 

710 







puls’less 

.912 

2 . 

777 

2 . 

720 







0.0 

.905 

16. 

390 

16. 

290 

6 

000 

2 

450 

145. 

0 

0.0 

.910 

16. 

720 

16. 

540 

6 . 

090 

2 

467 

146. 

7 

puls’less 

.904 

0 . 

716 

0 . 

713 







0.0 

.900 

6 . 

400 

6 . 

400 

8 . 

960 

2 . 

990 

199. 

0 

1.0 

.905 

6 . 

050 

6 . 

020 

8 . 

440 

2 . 

905 

190. 

5 

1.4 

.904 

4. 

963 

4. 

940 

6 . 

920 

2 . 

630 

163. 

0 

2.3 

.908 

2 . 

197 

2 . 

180 

3. 

060 

1 . 

750 

75. 

0 

4.2 

.913 

0 . 

917 

0 . 

904 

1 . 

263 

1 . 

125 

12 . 

5 

6.0 

.910 

0 . 

827 

0 . 

818 

1 . 

145 

1 . 

070 

7. 

0 

8.1 

.912 

0 . 

747 

0 . 

738 

1 . 

030 

1 . 

014 

1 . 

4 

9.7 

.912 

0 . 

743 

0 . 

733 

1 . 

027 

1 . 

013 

1 . 

3 


Note: — Puls’less = pulsationless. 








































































































APPENDIX C 


85 


TABLE 20 PER CENT ERROR FOR PITOT-METER, PULSATIONS 
QUIETED BY THROTTLING (SEE P. 42, PAR. 73) 


Date 

Run 

No. 

Pitot 

Used 

Drop 

Through 

Valve, 

Inches, 

Mercury 

Manometer Readings, 
Inches 

Ratio 


Error 

Per 

Cent 

Name 

Position 
of Tip 

At Orifice 
Head 

At Pitot- 
Meter 

Corrected 
to 0.9 

^Ratio 



1 

2 

3 

4 

5 

6 

7 

8 

9 

2-15-21 

1 

No. 1 

At 

puls’less 

0.901 

.1463 

.1462 





2 

Pitot 

Center 

0.025 

.900 

.1667 

.1667 

1.140 

1.068 

6.8 


3 



0.930 

.900 

.1557 

.1557 

1.072 

1.036 

3.6 


4 



1.930 

.899 

.1460 

.1470 

1.005 

1.003 

0.3 


5 



4.590 

.900 

.1535 

.1535 

1.050 

1.025 

2.5 


6 



6.540 

.899 

.1500 

. 1502 

1.028 

1.014 

1.4 


7 



7.010 

.902 

.1360 

.1357 

0.925 

0.962 

-3.8 


8 



8.160 

.903 

.1425 

.1421 

0.971 

0.985 

-1.5 


9 



9.820 

.901 

.1385 

.1384 

0.945 

0.972 

-2.8 


10 



12.060 

.908 

.1403 

.1392 

0.952 

0.975 

-2.5 


11 



puls’less 

.900 

. 1340 

. 1340 





12 



0.058 

.899 

.1540 

. 1550 

1.120 

1.058 

5.8 


13 



0.450 

.903 

.1505 

.1500 

1.082 

1.041 

4.1 


14 



0.850 

.900 

.1550 

.1550 

1.120 

1.058 

5.8 


15 



1.930 

.902 

.1405 

.1403 

1.046 

1.023 

2.3 


16 



4.180 

.912 

.1295 

.1280 

0.965 

0.983 

-1.7 


17 



5.900 

.895 

.1360 

.1370 

1.022 

1.011 

1.1 


18 



5.820 

.893 

.1540 

. 1550 

1.120 

1.058 

5.8 


19 



7.360 

.898 

.1425 

.1430 

1.069 

1.034 

3.4 


20 



9.640 

.901 

.1385 

.1384 

1.033 

1.017 

1.7 


21 



12.420 

.914 

. 1285 

.1266 

0.948 

0.974 

-2.6 

2-28-21 

22 

No. 1 

At 

puls’less 

.911 

2.10 

2.08 





23 

Pitot 

Center 

0.24 

.922 

2.42 

2.37 

1.140 

1.067 

6.7 


24 



0.48 

.919 

2.25 

2.21 

1.063 

1.031 

3.1 


25 



0.48 

.919 

2.20 

2.16 

1.038 

1.019 

1.9 


26 



0.75 

.902 

2.33 

2.32 

1.117 

1.057 

5.7 


27 



2.60 

.915 

2.05 

2.02 

0.972 

0.986 

-1.4 


28 



3.86 

.933 

2.32 

2.24 

1.078 

1.038 

3.8 


29 



6.40 

.930 

1.87 

1.81 

0.870 

0.933 

-6.7 


30 



8.35 

.928 

2.02 

1.96 

0.942 

0.971 

-2.9 


31 



12.85 

.944 

2.00 

1.91 

0.918 

0.958 

-4.2 

6-30-22 

32 

No. 1 

At 

puls’less 

.900 

0.982 

0.982 





33 

Pitot 

Center 

0.55 

.915 

5.60 

5.510 

5.610 

2.370 

137.0 


34 



1.05 

.913 

4.85 

4.780 

4.870 

2.204 

120.4 


35 



1.75 

.911 

3.52 

3.480 

3.545 

1.880 

88.0 


36 



3.30 

.912 

1.13 

1.115 

1.137 

1.065 

6.5 


37 



5.40 

.908 

0.85 

0.842 

0.856 

0.925 

-7.5 


38 



7.30 

.908 

0.89 

0.882 

0.897 

0.946 

-5.4 


39 



9.30 

.901 

0.96 

0.960 

0.976 

0.988 

-1.2 


40 



11.50 

.915 

1.03 

1.012 

1.030 

1.014 

1.4 


41 

No. 2 

At 

puls’less 

.904 

1.41 

1.406 



• . . 


42 

Pitot 

Center 

0.68 

.905 

5.80 

5.770 

4.120 

2.030 

103.0 


43 



1.50 

.904 

4.50 

4.480 

3.200 

1.788 

78.8 


44 



2.30 

.901 

2.73 

2.730 

1.950 

1.395 

39.5 


45 



4.30 

.912 

1.46 

1.440 

1.030 

1.015 

1.5 


46 



6.20 

.908 

1.41 

1.400 

1.000 

1.000 

0.0 


47 



8.20 

.912 

1.44 

1.420 

1.014 

1.007 

0.7 


48 



10.30 

.899 

1.48 

1.480 

1.057 

1.028 

2.8 


■49 



12.30 

.891 

1.49 

1.520 

1.082 

1.040 

4.0 


N ote: _Inclined manometer was used. To reduce Column 6 to inches of water, multiply 

by 0.17. 


































































































86 


EFFECT OF PULSATIONS ON FLOW OF GASES 


TABLE 21 DISTRIBUTION OF PULSATION AS SHOWN BY PITOT TRAVERSES 

(SEE P. 40, PAR. 67) 


Date 

Run 

No. 

Pitot Used 

Kind 

of 

Flow 

Manometer Readings, 
Inches 

Ratio 

VRatio 

Error 

Per 

Cent 

Name 

Position 
of Tip 

At Orifice 
Head 

At Pitot 
Meter 

1 Corrected 
to 0.9 



1 

2 

3 

4 

5 

6 

7 

8 

9 

6-30-22 

1 

No. 1 

.837r 

puls’less 

0.906 

0.660 

0.655 





2 

Pitot 

.837r 

pulsating 

.912 

6.060 

5.980 

9.13 

3.025 

202.5 


3 

Vertical 

.410r 

puls’less 

.908 

0.900 

0.892 





4 

Traverse 

.410r 

pulsating 

.915 

6.380 

6.280 

7.04 

2.655 

165.5 


5 


center 

puls’less 

.912 

0.970 

0.968 


. 

..... 


6 


center 

pulsating 

.906 

6.490 

6.450 

6.66 

2.580 

158.0 


7 


.410r 

puls’less 

.901 

0.840 

0.839 


. * 

..... 


8 


.410r 

pulsating 

.912 

6.440 

6.360 

7.58 

2.753 

175! 3 


9 


,837r 

puls’less 

.897 

0.610 

0.612 





10 


.837r 

pulsating 

.908 

5.630 

5.580 

9.12 

3.020 

202.0 




bottom 











right 









11 


.837r 

puls’less 

.905 

0.630 

0.625 



• • • • • 


12 

No. 2 

.837r 

pulsating 

.907 

4.630 

4.590 

7.34 

2.710 

171.0 


13 

Pitot 

.410r 

puls’less 

.900 

1.060 

1.060 





14 

Hori- 

.410r 

pulsating 

.910 

6.180 

6.120 

5.77 

2.400 

140.0 


15 

zontal 

center 

puls’less 

.904 

1.410 

1.406 





16 

Traverse 

center 

pulsating 

.908 

7.170 

7.110 

5.06 

2.247 

124.7 


17 


.410r 

puls’less 

.903 

1.470 

1.465 





18 

. 

.410r 

pulsating 

.909 

7.770 

7.590 

5.17 

2.275 

127.5 


19 


.837r 

puls’less 

.904 

1.070 

1.066 





20 


.837r 

pulsating 

.912 

7.280 

7.180 

6.74 

2.600 

160.0 




left 









Note: — To reduce Column 6 to inches of water, multiply by 0.17. 
r = radius of pipe. 















































APPENDIX C 


87 


TABLE 22 PER CENT ERROR FOR VENTURI METER, PULSATIONS 
QUIETED BY VOLUMES (SEE P. 43, PAR. 75) 


Date 

Run 

No. 

Volume Used 

Drop 

Through 

Volume, 

Inches, 

Water 

Manometer Readings, 
Inches of Water 

Ratio 

"'/Ratio 

Error 

Per 

Cent 

Diam., 

Inches 

Volume, 
Cu. Ft. 

At Orifice 
Head 

At Venturi 
Meter 

Corrected 
to 0.9 



1 

2 

3 

4 

5 

6 

7 

8 

9 


1 

8 06 


pnls’less 

0.900 

9.10 

9.10 





2 

8.06 

1.65 

3.0 

.900 

24.20 

24.20 

2.660 

1.630 

63.0 


3 

9 00 


puls’less 

.900 

9.68 

9.68 





4 

9.00 

0.33 

0.9 

.890 

29.36 

29.66 

3.175 

1.780 

78.0 


5 

9.00 

0.67 

0.9 

.899 

28.47 

28.48 

2.950 

1.717 

71.7 


6 

9.00 

1.00 

0.9 

.894 

25.43 

25.63 

2.660 

1.630 

63.0 


7 

9.00 

1.33 

0.9 

.891 

23.03 

23.25 

2.400 

1.550 

55.0 


8 

9.00 

1.66 

0.9 

.906 

20.30 

20.18 

2.090 

1.445 

44.5 


9 

9.00 

2.00 

0.9 

.886 

18.63 

18.94 

1.900 

1.378 

37.8 


10 

9.00 

0.33 

0.9 

.890 

29.33 

29.62 

3.060 

1.750 

75.0 


11 

9.00 

1.00 

0.9 

.909 

26.53 

26.27 

2.720 

1.650 

65.0 


12 

9.00 

2.00 

0.9 

.901 

22.70 

22.68 

2.350 

1.535 

53.5 


13 

94 00 


pijls’lpss 

900 

9.20 

9.20 





14 

24.00 

3.14 

0.0 

.909 

17.13 

16.97 

1.845 

1.360 

36.0 


15 

24.00 

6.28 

0.0 

.903 

12.60 

12.56 

1.365 

1.167 

16.7 


16 

24.00 

7.86 

0.0 

.899 

11.63 

11.64 

1.266 

1.125 

12.5 


17 

24.00 

15.73 

0.0 

.893 

9.75 

9.83 

1.062 

1.031 

3.1 


18 

36.00 

3.54 

0.0 

.909 

16.16 

16.00 

1.740 

1.320 

32.0 


19 

36.00 

10.62 

0.0 

.876 

10.70 

11.00 

1.196 

1.093 

9.3 


20 

36.00 

14.14 

0.0 

.900 

10.50 

10.50 

1.140 

1.068 

6.8 


21 

36.00 

24.75 

0.0 

.897 

9.57 

9.60 

1.043 

1.022 

2.2 


99 

48 00 



900 

9.68 

9.68 





23 

48.00 

3.00 

0.0 

.901 

15.13 

15.12 

1.563 

1.250 

25.0 


24 

48.00 

7.00 

0.0 

.895 

11.90 

11.97 

1.236 

1.110 

11.0 


25 

48.00 

17.00 

0.0 

.900 

9.97 

9.97 

1.030 

1.015 

1.4 


26 

48.00 

27.00 

0.0 

.880 

9.63 

9.85 

1.015 

1.007 

0.7 


27 

48.00 

36.00 

0.0 

.898 

9.83 

9.85 

1.0150 

1.007 

0.7 


Note: — Puls’less=pulsationless 












































88 


EFFECT OF PULSATIONS ON FLOW OF GASES 


TABLE 23 PER CENT ERROR FOR ORIFICE METER (SEE P. 43, PAR. 75) 
With 33% Orifice, Pulsations Quieted by Volumes 


Date 

Run 

No. 

Volume Used 

Drop 

Through 

Volume 

Manometer Readings, 
Inches of Water 

Ratio 

VRatio 

Error 

Per 

Cent 

Diam., 

Inches 

Volume, 
Cu. Ft. 

At Orifice 
Head 

At Orifice 
Meter 

Corrected 
to 0.9 



1 

2 

3 

4 

5 

6 

7 

8 

9 

8-18-21 

1 



puls’less 

0.900 

22.00 

22.00 





2 

24 

3.14 

0.0 

.898 

23.90 

23.94 

1.088 

1.043 

4.3 


3 

24 

6.28 

0.0 

.885 

22.60 

23.00 

1.045 

1.022 

2.2 


4 

24 

7.86 

0.0 

.874 

22.53 

23.20 

1.054 

1.027 

2.7 


5 

24 

15.73 

0.0 

.895 

22.80 

22.90 

1.040 

1.020 

2.0 


6 

36 

3.54 

0.0 

.894 

24.10 

24.23 

1.100 

1.049 

4.9 


7 

36 

10.62 

0.0 

.898 

22.80 

22.84 

1.040 

1.020 

2.0 


8 

36 

14.14 

0.0 

.882 

22.40 

22.86 

1.040 

1.020 

2.0 


9 

36 

24.75 

0.0 

.893 

23.00 

23.19 

1.053 

1.026 

2.6 


With 70% Orifice, Pulsations Quieted by Volumes 


1 

24 

1 

53 

puls’less 

0.900 

4 

.330 

4 

.330 







2 

24 

1 

53 

0.0 

.915 

11 

.130 

10 

930 

2 

.530 

1 

.590 

59 

.0 

3 

24 

3 

14 

puls’less 

.900- 

4 

250 

4 

.250 







4 

24 

3 

14 

0.0 

.890 

9 

.010 

9 

020 

2 

.125 

1 

.458 

45 

.8 

5 

24 

6 

28 

puls’less 

.900 

4 

.310 

4 

310 







6 

24 

6 

28 

0.0 

.897 

5 

220 

5 

230 

1 

.214 

1 

.100 

10 

0 

7 

24 

7 

86 

puls’less 

.900 

4 

290 

4 

290 







8 

24 

7 

86 

0.0 

.887 

4 

590 

4 

760 

1 

086 

1 

043 

4 

3 

9 

24 

15 

73 

0.0 

.913 

4 

780 

4 

710 

1 

096 

1 

048 

4 

8 

10 

36 

3 

54 

puls’less 

.900 

4 

330 

4 

330 







11 

36 

3 

54 

0.0 

.887 

8 

716 

8 

840 

1 

880 

1 

372 

37 

2 

12 

36 

10 

62 

puls’less 

.900 

4 

290 

4 

290 







13 

36 

10 

62 

0.0 

.878 

5 

020 

5 

150 

1 

200 

1 

096 

9. 

6 

14 

36 

14 

14 

puls’less 

.900 

4 

330 

4 

330 







15 

36 

14 

14 

0.0 

.896 

5 

780 

5 

800 

1 

340 

1 

160 

16 

0 

16 

36 

24 

75 

0.0 

.914 

4 

570 

4 

500 

1 

040 

1 

020 

2 

0 



















































APPENDIX C 


89 


TABLE 24 PER CENT ERROR FOR VENTURI METER, PULSATIONS 
QUIETED BY VOLUMES WITH ORIFICES (SEE P. 43, PAR. 78) 



Run 

Volume Used 

Drop 

Through 

Volume, 

Manometer Readings, 
Inches of Water 



Error 

Date 






Ratio 

VRatio 

Per 

No. 







Diam., 

Volume, 

Inches, 

At Orifice 

At Venturi 

Corrected 



Cent 



Inches 

Cu. Ft. 

Mercury 

Head 

Meter 

to 0.9 






1 

2 

3 

4 

5 

6 

7 

8 

9 

7-30-21 

1 

9.0 


puls’less 

1.70 

0.900 

9.68 

9.68 




2 * 

9.0 

0.33 

.887 

16.75 

17.00 

1.757 

1.322 

32.2 


3* 

9.0 

0.33 

2.80 

.886 

14.20 

14.59 

1.508 

1.228 

22.8 


4 

9.0 

0.33 

3.30 

*907 

11.70 

11.62 

1.201 

1.097 

9.7 


5* 

9.0 

0.33 

4.00 

.892 

12.56 

12.68 

1.310 

1.141 

14.1 


6 

9.0 

0.33 

5.40 

.893 

10.30 

10.39 

1.074 

1.035 

3.5 


7* 

9.0 

0.33 

6.60 

.907 

11.20 

11.12 

1.150 

1.071 

7.1 


8 

9.0 

0.33 

8.50 

.911 

10.03 

9.95 

1.025 

1.012 

1.2 


9* 

9.0 

0.33 

11.50 

.910 

10.63 

10.53 

1.089 

1.045 

4.5 


10 

9.0 

0.33 

12.60 

.888 

9.60 

9.73 

1.005 

1.003 

0.3 


11 * 

9.0 

1.00 

1.90 

.875 

13.33 

13.70 

1.417 

1.189 

18.9 


12 * 

9.0 

1.00 

3.10 

.913 

12.40 

12.23 

1.264 

1.124 

12.4 


13 

9.0 

1.00 

3.70 

.915 

10.50 

10.33 

1.068 

1.032 

3.2 


14* 

9.0 

1.00 

4.50 

.910 

11.03 

11.90 

1.127 

1.061 

6.1 


15 

9.0 

1.00 

5.80 

.888 

9.60 

9.72 

1.004 

1.002 

0.2 


16* 

9.0 

1.00 

7.10 

.960 

10.90 

10.22 

1.057 

1.027 

2.7 


17 

9.0 

1.00 

8.40 

.893 

9.57 

9.64 

0.996 

0.998 

-0.2 


18* 

9.0 

1.00 

11.20 

.917 

10.40 

10.21 

1.055 

1.026 

2.6 


19 

9.0 

1.00 

12.90 

.856 

9.20 

9.60 

1.000 

1.000 

0.0 


20 * 

9.0 

2.00 

2.10 

.921 

12.00 

11.73 

1.212 

1.100 

10.0 


21 * 

9.0 

2.00 

3.00 

.894 

10.53 

10.60 

1.096 

1.045 

4.5 


22 

9.0 

2.00 

3.70 

.930 

10.40 

10.07 

1.041 

1.020 

2.0 


23* 

9.0 

2.00 

4.60 

.911 

10.20 

10.08 

1.042 

1.020 

2.0 


24 

9.0 

2.00 

6.00 

.940 

10.20 

9.77 

1.010 

1.004 

0.4 


25* 

9.0 

2.00 

7.20 

.959 

10.57 

9.92 

1.024 

1.011 

1.1 


26 

9.0 

2.00 

8.20 

.911 

9.80 

9.69 

1.001 

1.001 

0.1 


27* 

9.0 

2.00 

11.40 

.911 

9.90 

9.79 

1.011 

1.005 

0.5 


28 

9.0 

2.00 

12.60 

.895 

9.50 

9.56 

0.988 

0.994 

-0.6 


29 

30 

24.0 

24.0 


puls’less 

3.50 

.900 

9.20 

9.20 





1.57 

.882 

9.55 

9.74 

1.058 

1.028 

2.8 


31 

24.0 

1.57 

5.50 

.881 

9.30 

9.49 

1.032 

1.016 

1.6 

8-15-21 

32 

24.0 

1.57 

7.60 

.881 

9.37 

9.57 

1.040 

1.020 

2.0 


33 

24.0 

3.14 

3.63 

.884 

9.27 

9.43 

1.025 

1.012 

1.2 


34 

24.0 

3.14 

5.52 

.912 

9.34 

9.23 

1.003 

1.002 

0.2 


35* 

24.0 

6.28 

2.59 

.905 

9.87 

9.82 

1.072 

1.035 

3.5 


36 

24.0 

6.28 

3.75 

.889 

9.03 

9.14 

0.993 

0.997 

-0.3 


37 

24.0 

6.28 

5.65 

.891 

9.15 

9.25 

1.005 

1.003 

0.3 


38 

24.0 

7.86 

2.00 

.903 

9.50 

9.47 

1.030 

1.015 

1.5 


39 

24.0 

7.86 

2.60 

.886 

9.20 

9.35 

1.015 

1.007 

0.7 


40 

24.0 

15.73 

2.07 

.894 

9.23 

9.29 

1.010 

1.005 

0.5 


41 

36.0 

3.54 

2.50 

.908 

9.70 

9.62 

1.046 

1.022 

2.2 


42 

36.0 

3.54 

2.93 

.916 

9.57 

9.41 

1.026 

1.013 

1.3 


43 

36.0 

3.54 

3.67 

.912 

9.20 

9.08 

0.988 

0.993 

-0.7 


44 

36.0 

3.54 

5.34 

.916 

9.37 

9.21 

1.000 

1.000 

0.0 


45 

36.0 

3.54 

5.94 

.879 

8.98 

9.19 

1.000 

1.000 

0.0 


46 

36.0 

10.62 

2.53 

.884 

9.17 

9.33 

1.014 

1.007 

0.7 


47 

36.0 

10.62 

2.94 

.904 

9.24 

9.20 

1.000 

1.000 

0.0 


48 

36.0 

10.62 

3.79 

.899 

9.13 

9.14 

0.994 

0.997 

-0.3 

8 -20-21 

49 

36.0 

10.62 

5.18 

.884 

9.03 

9.19 

1.000 

1.000 

0.0 

50 

36.0 

10.62 

5.59 

.885 

9.08 

9.23 

1.003 

1.002 

0.2 


51 

36.0 

14.14 

2.48 

.913 

9.20 

9.07 

0.987 

0.992 

-0.8 


52 

36.0 

14.14 

3.69 

.890 

8.90 

9.00 

0.978 

0.988 

-1.2 


53 

36.0 

24.75 

1.87 

.900 

9.30 

9.30 

1.011 

1.005 

0.5 


54 

36.0 

24.75 

2.54 

.900 

9.37 

9.37 

1.018 

1.009 

0.9 


55 

36.0 

24.75 

3.62 

.884 

9.10 

9.27 

1.007 

1.003 

0.3 

2 -8-22 

56 

57 

8.06 

8.06 


puls’less 

1.30 

900 

9.10 

9.10 



. . . 

1.65 

.900 

12.83 

12.83 

1.432 

1.204 

20.4 


58 

8.06 

1.65 

1.20 

.900 

13.00 

12.90 

1.480 

1.217 

21.7 


* Throttled by one orifice at entrance to volume. 


























































90 


EFFECT OF PULSATIONS ON FLOW OF GASES 


TABLE 25 PER CENT ERROR FOR ORIFICE METER (SEE P. 43, PAR. 78) 
With 33% Orifice, Pulsations Quieted by Volumes With Orifices 


Date 

Run 

No. 

Volume Used 

Drop 

Through 

Volume, 

Inches, 

Mercury 

Manometer Readings, 
Inches of Water 

Ratio 


Error 

Per 

Cent 

Diam., 

Inches 

Volume, 
Cu. Ft. 

At Orifice 
Head 

At Orifice 
Meter 

Corrected 
to 0.9 

"'/Ratio 



1 

2 

3 

4 

5 

6 

7 

8 

9 

8-19-21 

1 



puls’less 

0.900 

22.00 

22.00 




2 

24 

1.53 

3.31 

.891 

22.50 

22.70 

1.033 

1.016 

1.6 


3 

24 

1.53 

5.74 

.892 

22.30 

22.50 

1.023 

1.011 

1.1 


4 

24 

1.53 

7.60 

.909 

23.15 

22.90 

1.040 

1.020 

2.0 


5 

24 

3.14 

3.49 

.902 

21.93 

21.90 

0.994 

0.997 

-0.3 


6 

24 

3.14 

5.52 

.910 

23.02 

22.80 

1.037 

1.018 

1.8 


7 

24 

3.14 

5.62 

.908 

23.00 

22.81 

1.037 

1.018 

1.8 


8 

24 

3.14 

7.48 

.898 

22.50 

22.53 

1.023 

1.011 

1.1 


9* * 

24 

6.28 

2.63 

.904 

22.50 

22.40 

1.018 

1.009 

0.9 


10 

24 

6.28 

3.68 

.882 

21.60 

22.10 

1.004 

1.002 

0.2 


11 

24 

6.28 

5.65 

.894 

21.97 

22.10 

1.004 

1.002 

0.2 


12 

24 

7 86 

1.97 

.904 

22.72 

22.63 

1.030 

1.015 

1.5 


13 

24 

7.86 

2.53 

.891 

22.55 

22.79 

1.035 

1.017 

1.7 


14 

24 

15.73 

2.07 

.892 

22.38 

22.60 

1.027 

1.013 

1.3 


15 

36 

3.54 

2.50 

.907 

22.30 

22.08 

1.003 

1.002 

0.2 


16 

36 

3.54 

2.93 

.880 

21.17 

21.63 

0.983 

0.992 

-0.8 


17 

36 

3.54 

3.67 

.887 

22.06 

22.41 

1.020 

1.010 

1.0 


IS 

36 

3.54 

5.34 

.915 

22.28 

21.92 

0.996 

0.998 

-0.2 


19 

36 

3.54 

5.94 

.902 

21.90 

21.86 

0.994 

0.996 

-0.4 


20 

36 

10.62 

2.53 

.893 

21.60 

21.75 

0.988 

0.994 

- 0.6 


21 

36 

10.62 

2.94 

.896 

21.95 

22.06 

1.002 

1.001 

0.1 


22 

36 

10.62 

3.79 

.896 

22.25 

22.36 

1.015 

1.007 

0.7 


23 

36 

10.62 

5.18 

.885 

21.50 

21.86 

0.994 

0.996 

-0.4 


24 

36 

10.62 

5.59 

.914 

22.15 

21.95 

0.998 

0.999 

-0.1 


25 

36 

14.14 

2.48 

.900 

22.40 

22.40 

1.018 

1.009 

0.9 


26 

36 

14.14 

3.69 

.896 

22.20 

22.30 

1.013 

1.006 

0.6 


27 

36 

24.75 

1.87 

.905 

22.83 

22.75 

1.033 

1.016 

1.6 


28 

36 

24.75 

2.54 

.887 

22.35 

22.68 

1.031 

1.015 

1 .5 


29 

36 

24.75 

3.62 

.888 

22.30 

22.64 

1.030 

1.015 

1.5 


Note: — Puls’less = pulsationless. 

* Throttled by one orifice at entrance to volume. 











































APPENDIX C 


91 


With 70% Orifice, Pulsations Quieted by Volumes With Orifices 
TABLE 25 PER CENT ERROR FOR ORIFICE METER — Continued 


Run 

No. 

Volun 

Diam., 

Ins. 

ie Used 

Volume, 
Cu. Ft. 

Drop 

Through 

Volume, 

Inches, 

Mercury 

Manometer Readings, 
Inches of Water 

Ratio 


Error 

Per 

Cent 

At Orifice 
Head 

At Orifice 
Meter 

Corrected 
to 0.9 

'/Ratio 


1 

2 

3 

4 

5 

6 

7 

8 

9 

1 



puls’less 

0.900 

4.33 

4 33 




2 

24 

1.53 

3.32 

.883 

5.09 

5.18 

1.200 

1.094 

9.4 

3 

24 

1.53 

5.46 

.892 

4.61 

4.66 

1.077 

1.038 

3.8 

4 

24 

1.53 

7.64 

.911 

4.78 

4.73 

1.093 

1.046 

4.6 

5 



puls’less 

.900 

4.25 

4 25 




6 

24 

3.14 

3.64 

.900 

4.40 

4.40 

1.036 

1.018 

1.8 

7 

24 

3.14 

5.65 

.901 

4.28 

4.28 

1.010 

1.005 

0.5 

8 

24 

3.14 

7.78 

.906 

4.27 

4.24 

1.000 

1.000 

0.0 

9 



puls’less 

.900 

4.31 

4 31 




10 * 

24 

6.28 

2.78 

.886 

4.56 

4.63 

1.076 

1.038 

3.8 

11 

24 

6.28 

3.82' 

.892 

4.47 

4.51 

1.047 

1.023 

2.3 

12 

24 

6.28 

5.82 

.885 

4.41 

4.48 

1.041 

1.020 

2.0 

13 



puls’less 

.900 

4.25 

4.25 




14 

24 

7.86 

1.97 

.876 

4.23 

4.35 

1.023 

1.011 

1.1 

15 

24 

7.86 

2.61 

.910 

4.32 

4.27 

1.004 

1.002 

0.2 

16 



puls’less 

.900 

4.30 

4.30 




17 

24 

15.73 

2.07 

.906 

4.22 

4.20 

0.977 

0.988 

-1.2 

18 



puls’less 

.900 

4.33 

4.33 




19 

36 

3.54 

2.55 

.898 

4.93 

4.94 

1.140 

1.068 

6.8 

20 

36 

3.54 

2.95 

.909 

4.88 

4.83 

1.115 

1.057 

5.7 

21 

36 

3.54 

3.74 

.885 

4.44 

4.51 

1.040 

1.020 

2.0 

22 

36 

3.54 

5.38 

.888 

4.42 

4.48 

1.033 

1.016 

1.6 

23 

36 

3.54 

5.79 

.904 

4.50 

4.48 

1.033 

1.016 

1.6 

24 



puls’less 

.900 

4.34 

4.34 




25 

36 

10.62 

2.60 

.892 

5.10 

5.14 

1.183 

1.088 

8.8 

26 

36 

10.62 

3.01 

.880 

5.05 

5.16 

1.190 

1.090 

9.0 

27 

36 

10.62 

3.60 

.896 

5.04 

5.06 

1.166 

1.080 

8.0 

28 

36 

10.62 

5.17 

.916 

5.22 

5.14 

1.183 

1.088 

8.8 

29 

36 

10.62 

5.64 

.886 

5.06 

5.13 

1.181 

1.087 

8.7 

30 



puls’less 

.900 

4.33 

4.33 




31 

36 

14.14 

2.50 

.915 

4.52 

4.45 

1.028 

1.014 

1.4 

32 

36 

14.14 

3.71 

.905 

4.43 

4.41 

1.017 

1.008 

0.8 

33 

36 

24.75 

1.83 

.902 

4.46 

4.45 

1.028 

1.014 

1.4 

34 

36 

24.75 

2.53 

.905 

4.55 

4.53 

1.043 

1.022 

2.2 

35 

36 

24.75 

* 3.64 

.913 

4.58 

4.52 

1.041 

1.020 

2.0 


* Throttled by one orifice at entrance to volume. 



































































92 


EFFECT OF PULSATIONS ON FLOW OF GASES 


TABLE 26 EFFECT OF MUFFLERS FOR QUIETING MAXIMUM PULSATIONS 
WITH VENTURI METER (SEE P. 44, PAR. 80) 


Date 

Run 

No. 

Kind of Muffler 
and Location 

Drop 

Through 

Muffler, 

Inches, 

Mercury 

Kind 

of 

Flow 

Manometer Readings, 
Inches of Water 

Ratio 


Error 

Per 

Cent 

At 

Orifice 

Head 

At 

Venturi 

Meter 

Cor¬ 
rected 
to 0.9 

"'/Ratio 



1 

2 

3 

4 

5 

6 

7 

8 

g 

7-21-21 

1 

57 ft. from comp., 





• 









0 900 

9 35 

9.35 





2 

Powell auto muffler. . 

0.10 

pulsating 

.908 

21.70 

21.50 

2.300 

1.516 

51.6 


3 

Judd’s funnel muffler 

0.25 

pulsating 

.899 

8.92 

8.94 

0.957 

0.979 

-2.1 


4 



puls’less 

.900 

9.68 

9.68 





5 

New muffler (direct) 

6.40 

pulsating 

.892 

10.38 

10.47 

1.081 

1.039 

3.9 


6 

New muffler (reversed) 

9.70 

pulsating 

.890 

9.93 

10.18 

1.051 

1.024 

2.4 


7 

New muffler (direct) 

9.90 

pulsating 

.920 

10.63 

10.41 

1.078 

1.038 

3.8 


8 

43 ft. from comp., 







- 




27 ft fr^m mpfpr 


pills’lp.ss 

900 

9 10 

9.10 





9 

8 sect, muffler only. . 

0.25 

pulsating 

.906 

24.20 

24.05 

2.645 

1.623 

62.3 


10 

8 sect, muffler with 











special orifices.... 

2.00 

pulsating 

.905 

12.20 

12.12 

1.350 

1.160 

16.0 


11 

8 sect, muffler with 











special orifices.... 

3.70 

pulsating 

.900 

10.60 

10.60 

1.165 

1.080 

8.0 


12 

8 sect, muffler wfith 











special orifices.... 

4.90 

pulsating 

.901 

9.73 

9.72 

1.070 

1.034 

3.4 


13 

8 sect, muffler with 











special orifices.... 

4.70 

pulsating 

.911 

9.80 

9.70 

1.067 

1.032 

3.2 


14 

8 sect, muffler with 











special orifices.... 

4.70 

pulsating 

.910 

9.50 

9.40 

1.030 

1.015 

1.5 


15 

8 sect, muffler with 











special orifices.... 

3.20 

pulsating 

.920 

10.20 

10.00 

1.100 

1.050 

5.0 


16 

8 sect, muffler with 











special orifices.... 

2.10 

pulsating 

.914 

11.40 

11.24 

1.236 

1.110 

11.0 


17 

8 sect, muffler with 











special orifices.... 

2.30 

pulsating 

.905 

11.50 

11.45 

1.260 

1.123 

12.3 


18 

8 sect, muffler with 











special orifices.... 

1.20 

pulsating 

.908 

13.00 

12.90 

1.420 

1.193 

19.3 


19 

Muffler out. 

0.00 

pulsating 

.900 

31.47 

31.47 

3.490 

1.870 

87.0 

1 




















































APPENDIX C 


93 


TABLE 27 EFFECT OF PULSATIONS ON FLOW-METER IN “DEAD-END” LINE 

(SEE P. 46, PAR. 85) 


Date 

Run 

No. 

Line 

Closed 

at 

Point: 

Kind 

of 

Flow 

Static 
Pressure 
in Line, 
Inches, 
Water 

Manometer 
Readings, 
Inches of Water 

Ratio 


Error 

Per 

Cent 

Equivalent 
Flow 
Based on 
Puls’less 
Flow, 

Per Cent 

"^Ratio 

At 

Orifice 

Head 

At 

Meter 



1 

2 

3 

4 

5 

6 

7 

8 

9 


Venturi Meter 


6-29-22 

1 



puls’less 

9.96 

0.900 

9.29 






2 



pulsating 

13.40 

.900 

30.15 

3.250 

1.850 

85.0 



3 

8 ft. 


“dead-end” 

3.50 


1.91 

0.206 

0.454 


45.4 


4 

below 


“dead-end” 

7.90 


2.29 

0.248 

0.498 


49.8 


5 

meter 


“dead-end” 

13.40 


2.81 

0.303 

0.552 


55.2 


6 

\ 


“dead-end” 

20.70 


3.25 

0.350 

0.592 


59.2 


7 



“dead-end” 

40.80 


4.06 

0.437 

0.661 


66.1 

6-29-22 

8 



“dead-end” 

3.4 


3.85 

0.414 

0.644 


64.4 


9 



“dead-end” 

5.1 


7.87 

0.847 

0.920 


92.0 


10 

18 ft. 


“dead-end” 

8.0 


12.60 

1.358 

1.162 


116.2 


11 

below 


“dead-end” 

10.9 


14.83 

1.596 

1.262 


126.2 


12 

meter 


“dead-end” 

13.4 


16.10 

1.732 

1.315 


131.5 


13 



“dead-end” 

17.4 


17.63 

1.900 

1.378 


137.8 


14 



“dead-end” 

20.5 


18.26 

1.960 

1.402 


140.2 


15 



“dead-end” 

40.8 


20.43 

2.205 

1.484 


148.4 


16 

Without vol. 

puls’less 

9.96 

.900 

9.29 


...... 




17 

8 ft. below 

“dead-end” 

13.50 


2.47 

0.267 

0.516 


51.6 


18 

18 ft. below 

“dead-end” 

13.50 


8.52 

0.916 

0.957 


95.7 


19 

40 ft. below 

“dead-end” 

13.40 


15.33 

1.650 

1.283 


128.3 


20 

45 ft. below 

“dead-end” 

13.40 


10.00 

1.077 

1.038 


103.8 


33% Orifice Meter 


21 

22 

23 

8 ft. below 

puls’less 

pulsating 

“dead-end” 

27.7 

32.0 

.900 

.900 

22.00 

26.35 

0.86 

1.196 

0.039 

1.092 

0.198 

9.2 

19.8 

24 

18 ft. below 

“dead-end” 



6.03 

0.274 

0.522 


52.2 

25 

45 ft. below 

“dead-end” 



6.20 

0.281 

0.530 


53.0 

26 

8 ft. below 

“dead-end” 



-0.10 

0.0045 

0.021 


-2.1 

27 

18 ft. below 

“dead-end” 



0.69 

0.031 

0.176 


17.6 

28 

45 ft. below 

“dead-end” 



1.18 

0.054 

0.233 


23.3 















































































94 


EFFECT OF PULSATIONS ON FLOW OF GASES 


TABLE 27 — Continued 


Date 

Run 

No. 

Line 

Closed 

at 

Point 

Kind 

of 

Flow 

Static 
Pressure 
in Line, 
Inches, 
Water 

Manometer 
Readings, 
Inches of Water 

Ratio 


Error 

Per 

Cent 

Equivalent 
Flow 
Based on 
Puls’less 
Flow, 
Per Cent 

NRatio 

At 

Orifice 

Head 

At 

Meter 



1 

2 

3 

4 

5 

6 

7 

8 

9 


70% Orifice Meter 


6-28-22 

09 




9 8 

0 900 

4 95 





30 

8 ft. 


pulsating 

11.0 

.900 

25.75 

5.200 

2.280 

128.0 



31 

below 


“dead-end” 

7.9 


3.30 

0.667 

0.804 


80.4 


32 

meter 


“dead-end” 

11.3 


3.19 

0.645 

0.816 


81.6 

6-28-22 

33 


f 

“dead-end” 

3.63 


1.13 

0.230 

0.480 


48.0 


34 



“dead-end” 

5.80 


3.11 

0.628 

0.783 


78.3 


35 

18 ft. 


“dead-end” 

9.15 


5.98 

1.210 

1.100 


110.0 


36 

below • 


“dead end” 

11.10 


6.81 

1.375 

1.172 


117.2 


37 

meter 


“dead-end” 

17.30 


9.33 

1.865 

1.366 


136.6 


38 



“dead-end” 

23.10 


10.97 

2.215 

1.487 


148.7 


39 



“dead-end” 

40.80 


12.30 

2.480 

1.575 


157.5 

8 - 11-22 

40 




9 0 

900 

4 91 





41 

volume 


pulsating 

11.7 

.900 

25.45 

5.190 

2.280 

128.0 



42 

8 ft. below 

“dead-end” 

11.7 

• . • • 

4.22 

0.860 

0.930 


93.0 


43 

18 ft. below 

“dead-end” 

11.7 


-0.79 

0.161 

0.400 


-40.0 


44 

40 ft. below 

“dead-end” 

11.7 


8.31 

1.690 

1.300 


13.0 


45 

45 ft. below 

“dead-end” 

11.7 


8.18 

1.670 

1.290 


129.0 


46 

With volume 











18 ft. below 

“dead-end” 

11.7 


6.66 

1.357 

1.160 


116.0 


47 

45 ft. below 

“dead-end” 

11.7 


6.57 

1.339 

1.156 


115.6 


80% Orifice Meter 


6-28-22 

4S 

49 

50 

8 ft. below 

puls’less 

pulsating 

“dead-end” 

9.4 

10.8 

10.8 

0.900 

.900 

2.19 

15.54 

3.17 

7.010 

1.440 

2.655 

1.200 

165.5 

120.0 


51 

18 ft. below 

“dead-end” 

10.8 

.... 

4.62 

2.100 

1.448 


144.8 


90% Orifice Meter 


52 



puls’less 

8.9 

0.900 

0.458 





53 



pulsating 

9.6 

.900 

5.740 

12.53 

3.543 

254.3 


54 


f 

“dead-end” 

3.8 


0.990 

2.16 

1.470 


147.0 

55 

8 ft. 


“dead-end” 

6.6 


2.550 

5.56 

2.310 


231.0 

56 

below 


“dead-end” 

9.6 


2.550 

5.56 

2.310 


231.0 

57 

meter •< 


“dead-end” 

12.3 


2.860 

6.24 

2.500 


250.0 

58 



“dead-end” 

17.4 


3.110 

6.78 

2.600 


260.0 

59 



“dead-end” 

23.1 


3.210 

7.00 

2.640 


264.0 

60 


< 

“dead-end” 

40.8 


4.510 

9.82 

3.123 


312.3 

61 


f 

“dead-end” 

3.8 


0.54 

1.18 

1.086 


108.6 

62 



“dead-end” 

6.6 


2.62 

4.72 

2.172 


217.2 

63 

18 ft. 


“dead-end” 

9.5 


3.03 

6.61 

2.570 


257.0 

64 

below < 


“dead-end” 

12.4 


3.11 

6.78 

2.600 


260.0 

65 

meter 


“dead-end” 

17.2 


3.33 

7.26 

2.690 


269.0 

66 



“dead-end” 

23.1 


3.26 

7.11 

2.660 


266.0 

67 


\ 

“dead-end” 

40.8 


4.28 

9.26 

3.100 


310.0 


Note: — For runs 29 to 67 the inclined manometer was used. To reduce Column 5 to inches of water, 
multiply by 0.17. 































































































APPENDIX C 


95 


TABLE 28 EFFECT OF PULSATIONS ON FLOW-METERS IN “DEAD-END” LINE 

(SEE P. 46, PAR. 85) 


Date 

Run 

No. 

Line 

Closed 

Kind 

of 

Flow 

Static 
Pressure 
in Line, 
Inches, 
Water 

Manometer 
Readings, 
Inches of Water 

Ratio 


Error 

Per 

Cent 

Equivalent 
Flow 
Based on 

at 

Point: 

At 

Orifice 

Head 

At 

Meter 

"^Ratio 

Puls’less 

Flow, 

Per Cent 



1 

2 

3 

4 

5 

6 

7 

8 

9 




3-Inch by 1 

|-Inch Flange Nozzle-Meter 




6-27-22 

1 


puls’less 

pulsating 

13.0 

0.900 

5.59 





2 


16.3 

.900 

11.73 

2.100 

1.450 

45.0 



3 

8 ft. below 




meter. . . 

“dead-end” 

16.3 


0.70 

0.125 

0.354 

. . . 

35.4 


4 

18 ft. below 

“dead-end” 

16.3 


2.33 

0.416 

0.645 


64.5 


5 

45 ft. below 

“dead-end” 

16.3 


2.74 

0.490 

0.700 


70.0 


3-Inch by 1 5-Inch Flange Nozzle-Meter 


6-27-22 

6 


puls’less 

10.0 

0.900 

1.636 




* 


7 


pulsating 

11.4 

.900 

6.160 

3.770 

1.942 

94.2 



8 

8 ft. below 










meter... 

‘ ‘ dead-end ’ ’ 

11.5 

.... 

0.410 

0.250 

0.500 


50.0 


9 

18 ft. below 

“dead-end” 

11.5 

.... 

0.923 

0.564 

0.752 


75.2 


10 

45 ft. below 

“dead-end” 

11.5 

.... 

1.191 

0.728 

0.853 


85.3 

8 -10-22 

11 


pnls’less 

9.8 

.900 

1.690 






12 


pulsating 

11.5 

.900 

6.100 

3.610 

1.900 

90.0 



13 

8 ft. below 










meter... 

“dead-end” 

11.8 


0.386 

0.228 

0.478 


47.8 


14 

18 ft. below 











with vols. 

“dead-end” 

11.8 


1.108 

0.655 

0.810 


81.0 


15 

45 ft. below 











with vols. 

“dead-end” 

4.2 


0.366 

0.216 

0.465 


46.5 


16 

45 ft. below 











with vols. 

“dead-end” 

7.1 


0.597 

0.353 

0.594 


59.4 


17 

45 ft. below 











with vols. 

“dead-end” 

9.0 


0.790 

0.467 

0.683 


68.3 


18 

45 ft. below 











with vols. 

“dead-end” 

11.8 


1.097 

0.648 

0.805 


80.5 


19 

45 ft. below 











with vols. 

“dead-end” 

15.0 


1.321 

0.775 

0.880 


88.0 


20 

45 ft. below 











with vols. 

“dead-end” 

18.0 


1.450 

0.858 

0.926 


92.6 


3-Inch by 2-Inch Flange Nozzle-Meter 


6-26-22 

21 


puls’less 

9.3 

0.900 

2.767 






22 


pulsating 

9.6 

.900 

16.100 

5.920 

2.432 

143.2 



23 

8 ft. 

“dead-end” 

0 .5 


3.510 

1.265 

1.125 


112 5 


24 

below 

“dead-end” 

0.8 


6.867 

2.470 

1.570 


157.0 


25 

meter 

“dead-end” 

9.6 


3.640 

1.310 

1.175 


117.5 


26 


“dead-end” 

1 .5 


6.910 

2.490 

1.580 


158.0 

6-26-22 

27 

18 ft. below 

“dead-end” 

0.8 


5.083 

1.830 

1.353 


135.3 


28 

meter 

“dead-end” 

9.6 


3.747 

1.368 

1.170 


117.0 

6-26-22 

29 

45 ft. below 

“dead-end” 

0.8 

.... 

5.030 

1.820 

1.350 


135.0 


30 

meter, 

“dead-end” 

9.6 

.... 

3.717 

1.340 

1.160 


116.0 


Note: — For runs 21 to 39 inclined manometer was used. To reduce Column 5 to inches of water, 
multiply by 0.17. 































































































96 


EFFECT OF PULSATIONS ON FLOW OF GASES 


TABLE 28 EFFECT OF PULSATIONS ON FLOW-METERS IN “DEAD-END” LINE 

(SEE P. 46, PAR. 85) — Continued 


Date 

Run 

No. 

Line 

Closed 

at 

Point: 

Kind 

of 

Flow 

Static 
Pressure 
in Line, 
Inches, 
Water 

Manometer 
Readings, 
Inches of Water 

Ratio 


Error 

Per 

Cent 

Equivalent 
Flow 
Based on 
Puls’less 
Flow, 

Per Cent 

At 

Orifice 

Head 

At 

Meter 

"^Ratio 



1 

2 

3 

4 

5 

6 

7 

8 

9 


3-Inch by 2^-Inch Flange Nozzle-Metee 


31 

32 

33 

8 ft. below 

puls’less 

pulsating 

“dead-end” 

8.7 

9.4 

9.6 

0.900 

.900 

0.714 

6.400 

3.510 

8.960 

4.920 

2.990 

2.220 

199.0 

222.0 

34 

18 ft. below 

“dead-end” 

9.6 


2.920 

4.080 

2.020 


202.0 

35 

45 ft. below 

“dead-end” 

9.6 


3.050 

4.280 

2.070 


207.0 

36 

37 

8 ft. below 
with vols. 

puls’less 

“dead-end” 

8.5 

10.0 

.900 

0.740 

2.740 

3.700 

1.923 


192.3 

38 

18 ft. below 
with vols. 

“dead-end” 

10.0 


2.99 

4.050 

2.070 


207.0 

39 

45 ft. below 
with vols. 

“dead-end” 

10.0 


1.30 

1.760 

1.327 


132.7 












































APPENDIX C 


97 


TABLE 29 EFFECT OF PULSATIONS ON FLOW-METERS IN “DEAD-END” LINE 

(SEE P. 46, PAR. 85) 


Date 

Run 

No. 

Line 

Closed 

at 

Point: 

Kind 

of 

Flow 

Static 
Pressure 
in Line, 
Inches, 
Water 

Manometer 

Readings, 

Inches 

Ratio 


Error 

Per 

Cent 

Equivalent 
Flow 
Based on 
Puls’less 
Flow, 

Per Cent 

“'/Ratio 

At 

Orifice 

Head 

At 

Meter 



1 

2 

3 

4 

5 

6 

7 

8 

9 


Pitot Tube No. 1 


6-30-22 

1 


puls’less 

8.8 

0.900 

0.982 






2 


pulsating 

9.2 

.900 

6.450 

6.570 

2.560 

156.0 


6-30-22 

3 

8 ft. 

3.2 


0.660 

0.672 

0.820 


82.0 


4 

below 

“ dead-end” 

6.1 


2.040 

2.080 

1.445 


144.5 


5 

meter 


9.0 


1.910 

1.945 

1.393 


139.3 


6 



11.8 


2.400 

2.445 

1.560 


156.0 


7 



14.3 


2.720 

2.770 

1.663 


166.3 


8 



20.1 


3.140 

3.200 

1.782 


178.2 


9 



40.8 


4.680 

4.760 

2.180 


218.0 

6-30-22 

10 



3.7 


0.45 

0.458 

0.677 


67.7 


11 



6.1 


2.37 

2.415 

1.551 


155.1 


12 

18 ft. 


9.1 


3.30 

3.360 

1.830 


183.0 


13 

below 

“dead-end” 

11.8 


3.61 

3,680 

1.917 


191.7 


14 

meter 


14.5 


3.88 

3.950 

1.987 


198.7 


15 



20.5 


3.99 

4.065 

2.015 


201.5 


16 



40.8 


5.26 

5.350 

2.315 


231.5 

8-9-22 

17 


piils’less 

8.6 

.900 

0.935 





18 


pulsating 

9.2 

.900 

6.630 

7.100 

2.660 

166.0 


8-9-22 

19 

8 ft. below 

9.3 


0.62 

0.663 

0.815 


81.5 


20 

meter with 

“dead-end” 

15.9 


0.78 

0.834 

0.914 


91.4 


21 

volumes 


18.6 


1.18 

1.262 

1.123 


112.3 


22 



21.0 


1.36 

1.458 

1.208 


120.8 

8-9-22 

23 

18 ft. 


4.8 


2.55 

2.725 

1.650 


165.0 


24 

below 


T'.O 


2.71 

2.900 

1.702 


170.2 


25 

meter 

“dead-end” 

9.5 


3.05 

3 260 

1.805 


180.5 


26 

with 


12.3 


3.56 

3.810 

1.950 


195.0 


27 

volumes 


15.4 


4.02 

4.300 

2.075 


207.5 


28 



20.7 


4.19 

4.480 

2.220 


222.0 

8-9-22 

29 

45 ft. 


3.1 


2.36 

2.525 

1.590 


159.0 


30 

below 


5.0 


2.40 

2.570 

1.602 


160.2 


31 

meter 

“dead-end” 

9.3 


3.28 

3.510 

1.873 


187.3 


32 

with 


10.0 


3.47 

3.715 

1.926 


192.6 


33 

volumes 


12.7 


3.98 

4.260 

2.035 


203.5 


Pitot Tube No 


9 


8-9-22 

34 


puls’less 

8.8 

0.900 

1.315 






35 


pulsating 

9.6 

.900 

5.870 

4.460 

2.115 

111.5 

* , 

8-9-22 

36 

8 ft. 


6.7 


-0.56 

0.425 

0.652 


-65.2 


37 

below 


10.2 


3.36 

2.554 

1.600 


160.0 


38 

meter, 

“dead-end” 

12.9 


5.20 

3.950 

1.990 


199.0 


39 

with 


15.4 


6.23 

4.740 

2.178 


217.8 


40 

volumes 


20.8 


6.66 

5.060 

2.250 


225.0 

8-9-22 

41 

18 ft. 


4.9 


1.99 

1.512 

1.230 


123.0 


42 

below 


7.0 


2.13 

1.620 

1.272 


127.2 


43 

meter, 

“dead-end” 

9.8 


2.30 

1.749 

1.323 


132.3 


44 

with 


12.0 


2.47 

1.878 

1.370 


137.0 


45 

volumes 


15.1 


2.66 

2.020 

1.422 


142.2 


46 



18.0 


2.71 

2.060 

1.464 


146.4 

8-9-22 

47 

45 ft. 


4.8 


2.03 

1.543 

1.242 


124.2 


48 

below 

“dead-end” 

7.0 


2.15 

1.633 

1.278 


127.8 


49 

meter 


9.8 


2.41 

1.832 

1.353 


135.3 


50 



12.0 


2.54 

1.930 

1.390 

•' • 

139.0 


Note: — To reduce Column 5 to inches of water, multiply by 0.17. 



















































































98 


EFFECT OF PULSATIONS ON FLOW OF GASES 


TABLE 30 COMPARISON OF MANOMETERS UNDER SAME PULSATING FLOW 

CONDITIONS (SEE P. 38, PAR. 64) 


Date 

Run 

No. 

Kind 

of 

Mano¬ 

meter 

Static 
Pressure 
in Line, 
Inches, 
Water 

Manometer Readings, Inches of Water 

Kind of Flow 

Line Closed at Points: 

8 Ft. Below 
Meter 

18 Ft. Below 
Meter 

45 Ft. Below 
Meter 





Manometer Connections 





Direct 

Reversed 

Direct 

Reversed 

Direct 

Reversed 

Direct 

Reversed 



1 

2 

3 

4 

5 

6 

7 

8 

9 

10 


1 5-Inch Flange Nozzle Meter 


8-10-22 




puls’less 









1 

Vertical 

9.8 

1.527 









2 

U-tube 

9.8 

1.720 









3 

W ater 

9.8 

1.600 









4 

Mano- 

11.8 



-0.250 

-0.250 






5 

meter 

11.8 








0.875 





puls’less 









6 

Inclined 

9.8 

1.665 









7 

U-tube 

9.8 

1.655 









8 

Oil 

9.8 

1.680 









9 

Mano- 

11.8 



0.468 

0.525 






10 

meter 

11.8 



0.138 

0.251 






11 


11.8 





0 546 

negative 




12 


4.2 






-0.077 

-0.120 


13 


11.8 







0 544 

negative 





puls’less 








14 


9.8 

1.665 









15 

Inclined 

9.8 

1.650 









16 

One-leg 

11.8 



0.386 

0 327 






17 

Reser- 

11.8 



0.622 

2.665 






18 

voir 

11.8 





1.108 

0 114 




19 

Oil 

4.2 







0 366 

0 109 


20 

Mano- 

11.8 







1 117 

0.097 


21 

meter 

11.8 



-1.610 

1.720 





70% Orifice Meter 





puls’less 







22 

Vertical 

9.0 

0.713 








U-tube 


pulsating 

pulsating 






23 

Water 

11.7 

3.980 

4.160 






24 

Mano- 




0.070 

0.320 


. 


25 

meter 




0.460 

0.710 


26 







=*=0.500 




puls’less 






27 

Inclined 

9.0 

0.848 








U-tube 

Oil 

Mano- 









28 

meter 

11.7 



0.127 

-0.006 







puls’less 





29 

Inclined 

9.0 

0.835 

pulsating 

4.330 






30 

One-leg 

11.7 







31 

Reser- 

11.7 


0.718 

2.495 




32 

voir Oil 




1.132 

0.044 


33 

Mano- 








meter 








1.390 




puls’less 






34 

Vertical 

9.0 

0.813 







35 

U-tube 

11.7 



-1.432 

1.665 




36 

2-liquid 






1.540 


Mano- 









meter 




























































































































































































































































































APPENDIX C 


99 


TABLE 31 SHOWING RATIO OF P 2 TO (^Pi + ^D ) 2 FOR FLOW-METERS (SEE 

P. 47, PAR. 88) 


Date 

Run, 

No. 

Static 
Pressure 
in Line, 
Inches, 
Water 

Line 

Closed 

at 

Point: 

Manometer Readings, 

Inches of Water 

P 2 

Ratio =--13- 

(VPi+ Vd) 2 

Puls’less 

Flow 

Pi 

Pulsating 

Flow 

P2 

“ Dead-end” 
Flow 

D 

For 

8 Ft. 

For 

18 Ft. 

For 

40 Ft. 

For 
45 Ft. 



1 

2 

3 

4 

5 

6 

7 

8 

9 


Venturi Meter 


6-29-22 

1 

9.96 


9.29 







2 

13.40 



30.15 






• 3 

13.40 

8 ft. below 









t 

meter. . . 



* 2.64 

1 386 




4 

13.40 

18 ft. below 



16.10 


0 606 


8-11-22 

5* 

13.40 




8 52 


0.847 



6* 

13.40 

40 ft. below 



15 33 


0.624 


7* 

13.40 

45 ft. below 



10.00 




33% Orifice Meter 


6-27-22 

8 

11.70 


22.00 








9 

13.70 



26.35 







10 

13.70 

18 ft. below 



6.03 


0 508 




11 

13.70 

45 ft. below 



6.20 




0.514 

8-11-22 

12* 

13.70 

18 ft. below 



0.69 


0 864 



13* 

13.70 

45 ft. below 



1.18 




0.790 


70% Orifice Meter 


6-28-22 


8 - 11-22 


14 

9.80 


4.93 



15 

11.00 



25.60 


16 

11.00 

8 ft. below 



3 19 

17 

11.00 

18 ft. below 



6.68 

18 

11.00 

45 ft. below 



6.81 

19 

11.00 

18 ft. below 



4.22 

20 

11.00 

40 ft. below 



8 25 

21 

11.00 

45 ft. below 



8.25 


592 


095 

400 


865 


100 


0.865 


80% Orifice Meter 


22 

9.40 


2.19 






23 

10.80 



15.54 





24 

10.80 

8 ft. below 



3.16 

1.664 



25 

10.80 

18 ft. below 



4.62 


1.180 



90% Orifice Meter 


6-29-22 

26 

9 00 


0.458 







27 

9.50 



5.74 







28 

9 50 

8 ft below 



2.55 

1.110 





29 

9.50 

18 ft. below 



3.03 


0.984 





Volume replaced by 3-inch line. 






























































































































































































100 


EFFECT OF PULSATIONS ON FLOW OF GASES 


TABLE 31 SHOWING RATIO OF P 2 TO (^Pi + ^D)°- FOR FLOW-METERS (SEE 

P. 47, PAR. 88) —• Continued 


Date 

Run, 

No. 

Static 
Pressure 
in Line, 
Inches, 
W ater 

Line 

Closed 

at 

Point: 

Manometer Readings, 

Inches of Water 

P 2 

Ratio — _ 

(Vpj-f Vd )2 

Puls’less 

Flow 

Pi 

Pulsating 

Flow 

P 2 

“ Dead-end” 
Flow 

D 

For 

8 Ft. 

For 

18 Ft. 

For 

40 Ft. 

For 
45 Ft. 



1 

2 

3 

4 

5 

6 

7 

8 

9 


1 j-Inch Flange Nozzle Meter 


30 

13 00 


5.59 






31 

16 30 



11.73 





32 

16 30 

S ft helow 



0.70 

1.214 



33 

16 30 

1 8 ft below 



2 33 


0.813 


34 

16.30 

45 ft. below 



2.74 





1|-Inch Flange Nozzle Meter 






• 




• 



6—27—22 

35 

10 0 


1.663 








36 

11 .4 



6.130 







37 

11 4 

8 ft. below 



0.386 

1.680 




8-10-22 

38 

11 4 

8 ft. below 



0.410 

1.645 




39 

11 .4 

18 ft. below 



0.923 


1.210 




40 

11 4 

18 ft. below 



0.108 


1.117 




41 

11.4 

45 ft. below 



1.191 




1.090 


42 

11.4 

45 ft. below 



1.097 




1.120 


2-Inch Flange Nozzle Meter 


6-26-22 

43 

9.3 


2.767 








44 

9.6 



16.10 







45 

9.6 

8 ft. below 



3.640 

1.260 





46 

9.6 

18 ft. below 



3.750 


1.240 




47 

9.6 

45 ft. below 



3.717 




1.245 




2h- 

-Inch Flange Nozzle Meter 




6-27-22 

48 

8.4 


0.727 








49 

9.6 



6.40 







50 

9.6 

8 ft. below 



3.51 

0.862 





51 

9.6 

18 ft. below 



2.92 


0 975 




52 

9.6 

45 ft. below 



3.05 




0.947 

8-11-22 

53 

9.6 

18 ft. below 



2.74 

1 010 




54 

9.6 

45 ft. below 



2.99 


0.960 




Pitot Tube No. 1 


6-30-22 

55 

8.9 


0.982 








56 

9.2 



6.45 







57 

9.2 

8 ft. below 



1.91 

1.141 





58 

9.2 

18 ft. below 



3.30 


0.820 



8-9-22 

59 

8.9 


0.935 








60 

9.2 



6.30 







61 

9.2 

8 ft. below 



0.62 

2.040 





62 

9.2 

18 ft. below 



3.05 


0.863 




63 

9.2 

45 ft. below 



3.28 



0.852 





Pitot 

Tube No. 

2 



8-9-22 

64 

8.7 


1.315 








65 

9.8 



5.87 







66 

9.8 

8 ft. below 



3 36 

0.661 





67 

9.8 

18 ft. below 



2 30 

0.827 




68 

9.8 

45 ft. below 



2.41 



0.808 




























































































































































































































































APPENDIX C 


101 


TABLE 32 (SEE P. 43, PAR. 75). QUIETING EFFECT OF VOLUMES FOR 
VENTURI AND ORIFICE METERS 

Capacity of Volumes, Cu. Ft. 


0 

5 

10 

15 

20 

25 

Error, Per Cent (From Curve, Fig. 25) 

90 

22 

8 

4 

2 

1 


TABLE 33 (SEE P. 47, PAR. 86) APPARENT FLOW WHEN METERS ARE IN 
“DEAD-END” LINE UNDER STANDARD LINE PRESSURE CONDITIONS 



Point of Line Closure Below Meter, Feet 

Meter Used 

8 

18 

45 


Apparent Flow Based on Pulsationless Flow, Per Cent 

Venturi. 

58 

131 


33 % Orifice. 

19 



70% Orifice. 

81 

119 


80 % Orifice. 

120 

145 


90 % Orifice. 

239 

239 


i\" Flange Nozzle. 

49 

81 


Pitot No. 1. 

140 

181 

181 

Pitot No. 2. 

50 

136 

136 









































102 


EFFECT OF PULSATIONS ON FLOW OF GASES 


APPENDIX 


D, CURVES AND ILLUSTRATIONS 



Size of Orifice, Ratio Orifice Diam. to Pipe Diam., 
Percent. 


Fig. 33. Maximum Error for Orifice 
Meter. (See Table 16.) 



















APPENDIX D 


103 



Drop in Pressure by Throttling, Inches of Mercury. 


Fig. 34. Percent Error for Venturi 
Meter, Pulsations Quieted by 
Throttling. (See Table 17.) 


















104 


EFFECT OF PULSATIONS ON FLOW OF GASES 



Drop in Pressure by Throttling, Inches of Mercury. 

Fig. 35. Percent Error for Orifice 
Meters; Pulsation Quieted by 
Throttling. (See Table 18.) 





















APPENDIX D 


105 



Drop in Pressure by Throttling, Inches of Mercury. 


Fig. 36. Percent Error for Flange- 
nozzle Meter. Pulsations Quieted 
by Throttling. (See Table 19.) 



















106 


EFFECT OF PULSATIONS ON FLOW OF GASES 



2 4 6 8 10 12 


Drop in Pressure by Throttling, Inches of Mercury. 

Fig. 37. Percent Error for Pitot 
Meter. Pulsations Quieted by 
Throttling. (See Table 20.) 

























APPENDIX D 



Fig. 38. Effect of Varying the Shape 
of the Quieting Volume. (See 
Page 43, Paragraph 77.) 












































108 


EFFECT OF PULSATIONS ON FLOW OF GASES 



Drop in Pressure across Volumes, Inches of Mercury. 


Fig. 39. Effect of Throttling by 
Orifices Combined with Volumes, 
for Venturi Meter. (See Table 24.) 






















APPENDIX D 


109 



Drop in Pressure across Volumes, Inches of Mercury: 


Fig. 40. Effect of Throttling by 
Orifices at Entrance and Exit to 
Volumes, for Venturi Meter. (See 
Table 24). 


















110 


EFFECT OF PULSATIONS ON FLOW OF GASES 



Drop in Pressure acrossVolumes, Inches of Mercury. 


Fig. 41. Effect of Throttling by 
Orifices at Entrance and Exit to 
24-inch Volumes for 70% Orifice 
Meter. (See Page 43, Paragraph 78.) 




















Error, percent. 


APPENDIX D 


111 



Fig. 42. Relation of Error due to 
Pulsating Flow to Restoration of 
Pressure Beyond the Orifice 
Meter. (See Table 9, Page 39.) 


















112 


EFFECT OF PULSATIONS ON FLOW OF GASES 




INDICATOR ARRANGEMENT-(MECHANICAL OPERATION) 


COMPRESSOR 

CYLINOER 



INDICATOR 1L 


mmmr-i 


KEDUCING MOTION 
ATTACHED TO 
CRANK. SriAPF 


INDUCTION COIL. J 


QE T£N r 



T2 BATTERY*" 

Jj INDICATORS FOR VELOCITY DETERMINATION-(HAND OPERATED) 


u .imm f \ GWTATOr 

p^g Kuaw 


'detent SOLENOID to move 
PENCIL POINT 
/AGAINST DRUM 


TO PRIMARY OF INDUCTION COil'J 

D commutator. 


mi) 


INDICATOR. DRUM 

(2 DETENT MOTION AND 
SPARKING POINTS. 

INSULATED BLOCK 


SPAPK/NO POINT IN LINE 
WITH INDICATOR PENCIL POINT 
CONNECTEO To SECONDARY 
OF INDUCTION COIL 



U 


V i l li' " ’ i— s 


5-2Q'2l _DO Prieiev 


FIG 43. DETAILS OF ARRANGEMENT OF INDICATORS 






















































































I 'h 'y^ ; fj fcpi 


1. Some Observations on the Quality of Paving Brick 

2. The Coefficient of Expansion and Contraction of White Ware 
Body Mixtures 

3. A Study of the Rattler Test for Paving Brick 

4. Superheated Steam , 

5. Tests of Sand-blasting Machine 





11. The Present Status of the 

12. The Ohio Coal Supply 

13. Hardwood Distillation 

14. Laps and Lapping 

15. The Ohio Water Problem 

16. Congress of Human Engineering 

17. Chemical Examination of Natural Brines 
IS. The Flash and Burning Points of Kerosene-Gasoline Mixtures . 

19. Economical Utilization of Liquid Fuel 

20. The Thermal, Electrical, and Magnetic Properties bf Alloys 

21. Gum Determination in Sugar Products 

22 . Gasification of Ohio Coals. Preliminary Survey 

23. Standardization of Telephone Rates 


s O' WV*! JZf -U'Z 

/' ■ 

Natural Brines . . ■ . ' ' , • 

ints of Kerosene-Gasoline Mixtures . 

Liahid Fuel ' ' ' 




24. Effect of Pulsations on Flow of Gases 


If/. 

jiflj 
■ . ■ 




M: 


■ 


CIRCULARS: 




No. ' 

1» Storage Batteries 

2. Telephone Transmission 

3. Inductive Interference 

4. Opportunities in the Telephone Industry 

5. The Care of the Farm-house Telephone 

6. Gross Talks and Inductive Interference 

7. The Determination of Telephone Rates 

8. Automobile Hfeadlighting 


o. AutomoDii8 xieaauguti 
9. Telephone Service 

10. Radio Telephone Service 

11. The Ohio Consumers’ Coal Problem 















































